559 §^^mMmBim>tu/i:^ 



>y 1 



TECHNICAL SKETCHING 

and 

FREE HAND LETTERING 



NOTES ON 

Technical Sketching and Free Hand Lettering 

FOR ENGINEERING STUDENTS 



BY 

ALTON L. SMITH, M. S. 
Professor of Machine Design 
Worcester Polj-technic Institute 



PUBLISHED BY THE AUTHOR 

WORCESTER, MASS. 

1907 



LISKAfiYof C0N<3RFSS 
Swu Guuies R^&iveo" 

n piJCyrisM Entry 

Class A KXc, No. 

•■ -'COPY B. 



i* 



Copyright, 1907. 

By Alton L. Smith, M. S., 

Worcester, Mass. 



PREFACE 

The modern engineer must know how to make drawings in order to know how to read them. Very Uttle 
of his time is spent at the drafting board, however. His drawings consist chiefly of sketches showing his ideas 
in more or less detail which are turned over to subordinates to be worked out and put in the conventional form. 

In the solution of his engineering problems, he is obliged to think in three dimensions and a preliminary 
sketch stands in the place of a model which he can work over and examine in order to clarify and fix his ideas. 
Such sketches must often be made in great profusion, and dexterity with the pencil is frequently an inspiration 
to the brain. 

One of the primary functions of a course in drawing is to cultivate and extend the faculty of thinking in 
space. To accomplish this successfully, the draftsman must learn how to express his ideas quickly and accu- 
rately. It is the purpose of this book to suggest how this may be done. 

Worcester, Aug. 23, 1907. Alton L. Smith. 



CONTENTS 

Chapter I. page 
Description of Methods of Representation 5 

Chapter II. 
Working Drawings 14 

Chapter III. 
Miscellaneous Details of Construction 31 

Chapter IV. 
General Suggestions on Technical Sketching 46 

Chapter V. 
Sketches for Working Drawings 52 

Chapter VI. 
Geometric Perspective and Artists ' Perspective 55 

Chapter VII. 
Axometric Sketching 62 

Chapter VIII. 
Isometric Drawings and Cabinet Projections 70 

Chapter IX. 
Comparison of Methods of Representation 74 

Chapter X. 
Free-Hand Lettering 76 



CHAPTER I 

DESCRIPTION OF METHODS OF REPRESENTATION 

1. Probably the best way to describe a material thing is to make a picture of it, and a written language 
composed of hieroglyphs would prove satisfactory if it had to express only what we sense through the eyes. 
To depict odours, sounds or emotions would severely tax such a language as reference to the ancient Egyptian 
monuments will prove. 

The written language of modern engineering construction has to deal chiefly with shape and size of material 
things. It is a picture language and its superiority over the language in common use will be quickly recognized, 
if one attempts to read a written description of a modern machine without the aid of an illustrative drawing. 

A perusal of legal documents will show how difficult it is to express an idea or fact concisely and with 
exactness. In the modern sciences, extended terminologies permit this. There is, of course, a special vocab- 
ulary of technical terms used by engineers and shop workmen, and it would be possible to write a specification 
describing each part of a machine so it could be built, but to write and to read such a description would be a 
tedious and a costly process involving many chances for error. There was a time when construction was carried 
on in shops by oral directions from the foreman, or the workman made a part of a machine to suit his own notions, 
very much as some repair work is now done. If such methods had prevailed, the general use of our numerous 
modern contrivances would have been deferred to the remote future. 

2. An engineering drawing must describe the machine or structure completely, exactly and concisely 
that it may insure economy of time for the maker and the reader. Most drawings used in engineering work 
are made mechanically with instruments, because most of them can be thus made more economically. There 
are, however, many drawings which an engineer or draftsman has to make, where it would be very impracticable 
to make them with instruments. Such are the innumerable preliminary sketches used in designing, the inciden- 
tal sketches made for illustrative or explanatory purposes, sketches of parts of existing machines and sketches 

S 



for work of which no record is preserved such as repair jobs. It is also true that some desirable forms of repre- 
sentation which can be made well and quickly free-hand, become expensive when drawn with instruments. 

3. The problem in illustrative drawing is to produce a representation of an object having three dimensions 
on a flat surface having only two dimensions. The difficulty lies in properly representing the third dimension. 
The different methods for accomplishing this, their underlying principles and their adaptation for mechanical 
and free hand treatment will be considered. 

Nearly all simple objects can be represented without ambiguity by a single outline drawing. A stick of wood 
looked at endwise tells nothing regarding its length. It might be a block or a long beam. By looking at it from 
some other point of view its true proportions are indicated. In the case of a sphere the outline from any point of 
view is a circle. There are three ways of completing this representation. If we draw a circle and write "sphere " on 
it, the size and shape are defined. If we draw two circles and indicate that these are views from two different points, 
the object is defined. If we draw a circle and shade its surface to represent the light and shade effect on the original, 
the object is defined. Each method has its advantages dependent on the use to which the drawing is put. 

4. If a die is held close to the face, but far enough from the eyes to be seen distinctly, it will appear 
as in Fig. i, A. On closing the right eye it appears as at B and on closing the left eye, as at C. The fact is, 

^ S Q we get a separate image of the object with each eye and if both eyes are open the 

two images are mei'ged more or less into one. To test this, set up a card about 10 
inches high edgewise between B and C and look at the figures from the top edge, 
the card serving as a partition to shield B from the right eye and C from the left. 
These two images will always occur when both eyes are used, but the difference 
between the two is not noticeable, except when the distance of the object from the 
eye is small as compared with the greatest horizontal dimension of the object. A drawing like A would not 
be a satisfactory representation of the die, but either B or C would be satisfactory. We therefore derive the 
conclusion that to make a satisfactory representation of an object, it should be drawn as seen with one eye. 
It is also true that if this dz'awing is to produce the same effect on the eye that the original object did, it 
should be looked at with one eye, the drawing being held at the same distance from the eye as when made. 




Fig. 1. 



Stereoscopic photographs made in pairs and viewed in the stereoscope give an increased reaUty to the third 
chmension. A similar effect is produced when a single pictm'e is viewed with one eye through a conical^tube, 
or thi'ough the closed hand. 




Actual DfiAw/Nq 
ON Pictu/^e: Plane: 



Fig. 2. 

5. Referring to Fig. 2, A, we have a cube ABCD-H resting on the right end of the top of a table OPQ. 
Let the eye be placed at E and interpose a transparent piece of glass KLMN between it and the cube. The 

7 



cube is visible to the eye, because light is reflected from its faces and as these faces have different degrees of 
illumination, their bounding edges appear conspicuously as lines. We may consider that the light reflected 
from any point, B, on the cube to the eye passes along a straight line, BE, through the glass at some point b. 
If we mark this point, b, on the glass, it will shut off our view of the corner, B, of the cube which is in line with 
it. In the same way, we may mark the other points on the glass where we see the other corners of the cube. 
These points are now connected forming lines which appear to coincide with the edges of the cube. That is, 
line ab shuts off edge, AB, be shuts off BC and in the same way, the others. The cube could now be removed 
and the figure abcd-h would produce the same effect on the eye that the edges of the cube did. It stands in 
place of, or represents the cube. Such a drawing is called a Linear Perspective. It is designated Linear because 
it represents lines, but not the light and shade nor the color efl'ect. 

Fig. 2, B, is the actual drawing, as it is on the glass plane. The 
transparent plane is called the picture plane. The line ES from the eye 
to the center of the object is called the line of sight. 

6. If in Fig. 2, A, the picture plane is revolved about the line X-Y as an 
axis, until it is perpendicular to the line ES, the perspective drawing would 
change to that shown in Fig. 3, A. Here the upright edges are not quite ver- 
tical and produce a false impression regarding the object. If they are made 
vertical, as in Fig. 3, B, the drawing will be an Artists' Perspective of the cube. 

7. Referring again to Fig. 2, A, suppose the eye to be moved along the line SE so that it is much further 
away from the object. Then the angles which the light rays make with each other at E would become much 
less. If E were removed along SE to a very great distance, then the angle between the light rays would reduce 
practically to zero and the light rays would become practically parallel. The drawing on the picture plane 
would be called an Oblique Projection. It is so called, because if we projected, or threw on the picture plane, 
each point of the object by a series of parallel lines oblique to the picture plane, we should get the same result. 

8. If the cube in Fig. 2, A, were placed further to the left with its front face parallel to the picture plane 
the perspective drawing of it would be like Fig. 4, A. If an oblique projection were now made by removing 

8 




Linear 

PLRSPECnyE 




Artists' 
Perspective 



Fig. 3. 



the eye to a great distance, the drawing would be Uke Fig. 4, B. Such a drawing is called a Cabinet Projection. 

Its peculiar features are that one face of the object is shown in its true size 
and shape, while lines perpendicular to this face appear inclined at 45° 
and of one-half their true length. 




Fig, 4. 



a 6 


y 


OfiTHOQfiAPHIC 

Projection 




d c 


h 



Fig. 



9. Referring again to Fig. 2, A, suppose the eye be removed to a 
great distance from the object along a line RE which is perpendicular to 
the picture plane. The light rays from the object 
to E would then become practically parallel to RE 
and therefore perpendicular to the picture plane. 
The drawing on the picture plane would then become like Fig. 5 and it would be called 
an Orthographic Projection, because if the object were projected on the picture plane by 
lines perpendicular to that plane, we should get the same result. The term projection 
is always understood to mean orthographic projection unless otherwise stated. It is 
thus apparent that a projection drawing is merely a perspective drawing in which the 
eye is placed at a great distance from the object. 

10. In Fig. 6, A, the cube, ABCD-H, is elevated slightly from the table and tm-ned so all its edges are 
obliciue to the plane of projection. It is also placed so its upright edges are all parallel to a side plane, not shown, 
but which is perpendicular to the table top and the plane of projection. If a projection of the cube is now made 
on the vertical plane, its actual shape will be like Fig. 6, B. If this drawing be compared with Fig. 2, B, a 
marked similarity is noticed, although there are also important differences. A projection made in this way 
is the basis of an Axometric Drawing. 

11. If the cube in Fig. 6, A, had been placed so that the three edges meeting at a corner, as for instance 
B, were equallj^ inclined to the plane of projection, then the resulting drawing would have been like Fig. 6, C. 
This is called an Isometric Projection. Its peculiar features are that the three edges meeting at B are 120° 
apart and eciual in length. Any line of the drawing, as for instance, be, is shorter than the edge of the cube 
it represents. 



9 



12. If a drawing were made of the cube, which was exactly Uke Fig. 6, C, in shape, but in which the 
Hnes be, ab, bg etc. were each equal to the true length of the edge of the cube then we should have an Isometric 
Drawing. An isometric drawing is exactly like an isometric projection, but larger. 



/SOM£T/flC PhOJECTJON 




Fig. 6. 



13. Solids have three principal dimensions; length, breadth or width and thickness or height. These 
terms are applied in various ways, depending on whether the object is large or small, movable or fixed and other 



10 



characteristics. The essential thing to remember is that these three dimensions are perpendicular, each to the 
others. It might be difficult to agree on the length, breadth and thickness of so irregular a form as a potato, 
but three measurements could be arbitrarily assumed, which would have the essential feature of such dimensions, 
namely, mutual perpendicularity. In the case of most artificial forms, however, there is little difficulty in select- 
ing these principal dimension lines or reference axes of measurement. Generally they will be partly or entirely 
determined by the physical peculiarities of the object. The rectangular block and the circular cylinder are 
the predominant artificial forms. In the former, the edges, and in the latter the axis of S3aTimetry and two per- 
pendicular diameters would be selected. In the case of the sphere, three perpendicular diameters would be chosen 
If a drawing is to be useful as a guide in construction, it must satisfy the following conditions. 

First, it must give an idea pictorially of the shape of the object. 

Second, it must be of such a nature that all necessary dimensions and specifications can be appended. 
Third, when completed with all dimensions and specifications, the whole must be capable of being read with 
a minimum amount of study. 

14. To permit satisfactory application of dimensions, the object must be placed so its projections show 
the lines of the object in their true length. To accomplish this, the object must be placed so two of its principal 
dimensions are parallel to the plane of projection. The result of this is to lose the third dimension, so that 
nearly always two or more projections of the object are required. 

In Fig. 7, the object to be represented is a triangular pyramid JKL-0. It is placed inside a glass box 
ABCDEFGH, the back side of which is lacking. A working drawing for such an object should give the size 
and exact shape of the base, the length of the altitude and the location of the vertex relative to the base. The 
pyramid is therefore placed with its base parallel to the top face of the box and this location brings the altitude 
parallel to the front face of the box. One side of the base, JK, is parallel to the face BCFG. The pyramid 
is now projected onto each of the five faces. The joints of the box along edges AE, BF, CG and DH are then 
broken. Keeping the front face, ABCD, stationary, swing the top, bottom and two side faces about their hinge 
lines AB, CD, BC and AD, until they come into the same plane with the front face, as shown. 
II 



Third Angle 
Projection _ 




Fig. 7. 



15- The projection figures on the four revolved faces are now grouped about the central projection on 
the front face and certain features of their relations should be noted. 

Considering the central projection, or front view, the principal one, it is seen that the view obtained 
from above the object, that is the top view, is placed above the front view; the view of the right side is placed 
at the right ; the bottom view below and the left view at the left of the front view. This is a logical arrange- 
ment and it is called third angle arrangement, or Third Angle Projection. 

This is the arrangement of views used in nine-tenths of the drafting rooms in the United States. The 
other arrangement most used is known as first angle projection. With this method of grouping, the top view 
is placed below the front view, the bottom view above, the right view at the left and the left view at the right. 
It is entirely illogical, renders a drawing more difficult to construct and to read and has advantages in only a 
few instances. First angle projection is used for shop drawings in Great Britain, on the continent and by the 
other tenth of draftsmen in the United States. 

i6. It should be noted next, that any point of the object, as the vertex 0, will have its projections in 
the front, left and right views, that is 0^, 0* and 0'^ on the same horizontal line. Also any point, as 0, will 
have its projections in the front top, and bottom views, that is, 0^ , 0^ and 0^ on the same vertical line. This 
relation between the views is a very important one, and it facilitates greatly the making and reading of the pro- 
jections. 

17. Inspection of the projections shows that two views, the front and top would suffice in this case to 
represent the object, and accommodate all necessary dimensions. Thus the top view shows the exact size and 
shape of the base and the location of the vertex, while the front view gives the exact altitude. Though two 
views are really necessary here, for some objects, one view would suffice. On the other hand, for some very 
irregular machine parts, five views supplemented by auxiliary sections, dotted lines and specifications are none 
too many, to make them intelligible. 

13 



i8. The names used in Fig. 7 for the different projections are those commonly employed. Others are 
also in use for architectural drawings and Descriptive Geometry. They are given in the following table. 



Common Name 

Front View 
Top View 
Right View 
Left View 
Bottom View 



Architectural Drawings 

Front Elevation 

Plan 

Right Elevation 

Left Elevation 

Plan 



Descriptive Geometry 

Vertical Projection 
Horizontal Projection 
Right Profile Projection 
Left Profile Projection 
Aux. Horizontal Projection 



CHAPTER II 

WORKING DRAWINGS 

19. A working drawing is one used by a workman in actually making the machine or structure which 
it represents. 

20. While many of the methods of representation described in the preceding chapter might be used 
for working drawings, the one last described is usually employed. Though somewhat deficient pictorially it 
has the following advantages. The process of making the projections is easily explained and generally under- 
stood. The drawings are composed principally of horizontal and vertical straight lines and circles, all of which 
are easily made with ordinary instruments. The large number of views available makes it possible to avoid 
the confusion of lines and figures which occurs when one view only is used. 

21. There are two kinds of working drawings. A detail drawing shows each piece by itself with complete 
dimensions and specifications for its construction as shown in Fig. 10. An assembly drawing shows all the parts 
of a machine or structure assembled, or put together : Or it may show a group only of parts put together. A 
drawing of an engine would illustrate the first, while a drawing of the connecting rod of an engine would illus- 
trate the second. An assembly drawing may be used in a pictorial way, merely, to give a general idea of the 

H 



machine, in which case, much of hidden detail is not indicated and only the principal dimensions are given. 
Such a drawing may be used for assembl ng or for erecting the machine and then everything is shown in 
greater or less detail, but with only a few dimensions. An assembly drawing may be used as a shop drawing 
for actual construction, and then complete dimensions are given for every detail. It is obvious that only the 
simplest machines, tools or structures could be thus drawn. A shaft hanger or an arbor press would be 
illustrations. Such a drawing has an advantage over a detail drawing, in that there is less chance of error, 
both in making the drawing and in making the parts. In the case of the draftsman, the drawing helps to 
check the dimensions and in the case of the workman, he sees how the parts fit together. If a machine is 
made on the interchangeable system, this last feature is of no particular value. 

22. Scale. Drawings should be made large enough so they can be easily and accurately read when 
covered with dimensions. For convenience in filing, most drafting departments have adopted standard sheet 
sizes, which are particularly adapted to their special line of work. 

It is often desirable to place on one sheet all the parts of a machine constituting a natural group; for 
instance, all the parts of the tailstock of a lathe; or all the forgings; or all the castings. These conditions, there- 
fore, will usually determine the scale. A bridge is drawn to a greatly reduced scale, the general run of machine 
parts are made full size, while instruments or machines with exceedingly small parts, like those of a watch, should 
be drawn larger than full size. 

23. The scales in common use are as follows, 12 inches, 6 inches, 3 inches, 1^ inches to one foot for ordinary 
details of machinery; 1 inch, f inch, ^ inch, | inch, I inch and |- inch to one foot for larger structural work. A 
drawing made to a scale of 1^ inches to one foot is one in which 1 J inches on the drawing represents one foot in 
the object; that is, the drawing is I of full size. Full size is a very desirable scale, especially for the designer, 
because it conveys an exact idea of the size of the part and there is also less liability of errors in dimensioning. 

SELECTION OF VIEWS 

24. Select those views and the least number of views that will completely and clearly represent the 
object. Do not use two views, if one will suffice. If more than one view is necessary, one of them should be 

IS 



the front view, as this makes it possible to project from points in one to corresponding points in the other projection 
by horizontal or vertical projecting lines. In Fig. 7 the object might have been placed so as to make a front view of 
what is now the right view. A corresponding change in the positions of the other views would have been necessary. 
A judicious use of dotted lines or of sections will often permit a reduction in the number of views, as 
is explained in Sections 29 and 30. The pipe fittings in Fig. 14, the Latch Handle in Fig. 8, A and the Spur 
Gear in Fig. 13 illustrate this. On the Lag Screw in Fig. 11, by specifying Sq. Head, an additional view is 
avoided. Also in the Anchor Bolt for concrete in Fig. 11, by giving the letter d after the |" dimension, a round 
bar is indicated thus making one view sufficient. 

25. While limitations of space or the clearness of the drawing may sometimes decide otherwise, yet 
the desirable and the customary front view is that view which shows the object most characteristically and in 
a natural position. For a building, it would be the facade; for a bridge, the longtitudinal view; for a pulley, 
the view showing the radiating arms; for a machine, the view a workman gets as he stands at work before it. 
Some objects have no characteristic view, others have several and a moving part like the crank on an engine 
may have many natural positions. These are exceptional. 

26. It is allowable to have one view showing the object with a part removed as in the Cylinder Cap, 
Fig. 10, while another view may show it entire or with a different part removed as in the Worm Gearing, Fig. 
13. To condense a drawing, it is often desirable to break out a portion as in the Pulley, Fig. 10. Under Broken 
Ends in Fig. 8 is indicated how to break rods, pipes, structural steel etc., so as to suggest the shape of the cross-section. 

An auxiliary view is sometimes needed which cannot be properly grouped with the other views. Its 
location or relation to the others must be very definitely specified by projecting lines or otherwise. 

27. When two pieces are exactly alike except in some minor detail or dimension, it is often possible to 
make one drawing serve for both, as in the Hoist Arm Yoke, Fig. 10. 

28. Threaded Parts are so numerous that to save the draftsman's time they have been conventional- 
ized. The same is true regarding Riveting in Structural Work, and the Fittings in Pipe Systems. These are 
represented in Fig. 11 and Fig. 14. 

16 



USE OF DOTTED LINES. 

29. Some draftsmen show all hidden edges, but this is plainly a mistake, for in many instances it produces 
only a confusion of lines and obscures the meaning of the drawing. Hidden edges should be shown, only when 
they contribute to the clearness of the drawing or give it a more finished appearance. Thus in Bevel Gears, 
Fig. 13, the dotted lines complete the representation partly shown by the half section. See also Section 83 for 
the proper way of making a dotted line. Figures 10, ir, 13 and 14 illustrate the use of dotted lines. 

USE OF SECTIONS. 

30. A slice or section is used to show the contour of an irregular shape or of a shape not clearly shown 
by dotted lines. The section of the puhey arm, Fig. 10, and of the Latch Handle, Fig. 8, A, are illustrations. 
The section may be specified in any- one of the three ways shown in Fig. 8, A. A section of this kind shows 
nothing more than the figure cut from the object by the sectioning plane. 

31. A sectional view is one which shows not only the cut surfaces, but everj^hing back of them also. 
The chief use of a sectional view is to explain the internal construction of the object. In Fig. 8, B, is an illus- 
tration of this. Note that the center is not cut, as there is nothing inside of it to be explained. Sectioning planes 
may be taken in any way to facilitate the explanation of the object, but they are usually taken parallel to some 
one of the planes of projection. Unless the location of the cutting plane is perfectly obvious, it should be indi- 
cated by its projection on the plane to which it is perpendicular, where it will be shown as a line, marked as 
in Fig. 8, A. 

32. Sometimes when it is not desirable to remove the part of the object in front of the sectioning plane, 
a dotted section may be used as in Fig. 14, V. 

33. Section lining or cress hatching may be at any angle, so long as it is not parallel to the bounding 
lines of the surfaces sectioned. The angles generally used are 30°, 45° and 60°, which taken both ways give 
six directions. If two different pieces come together in the same section, as in Fig. 8, B, a different angle should 
be used for each piece; but for different parts of the same piece, even though disconnected, the same sectioning 

17 



Cast Iron 





Use of Sections 



Babbitt 




Y^TPTTA 



Brick Wood 




Rubble. 







Concrete 



*» 



:0 



o-o 



V<i' 






i^^^-yAC^:^^^." 



*> g 



.'O* 



.0:0'= 



r>i 



Sand 



EAF!TH 



Water 




Broken Ends. 



I /^ 




B£AM 

-' ^-tH 


k 


' •» 

CHANNE.L 

irf 




Pipe 



Wood 



N 



Angle 



Tee 



r^ Max. Space Width 

^^ FOf< A QIVEN WIDTH 



v-\ Section 
AT MN 



Z Bah 



A Sectional i//£i/v 

Cross Lm/nq or o/rrsReA/T pa^ts 







OF AREA. 






\ \ \ ^ 


\\ 


^v 


\\^ 


\^ 


^r 


h\\\^ 


\\ 



3£CT/o/v LiNiNq McjT A/or 




Fig. 8. 



will be used. Width of spacing is determined by the smallest sectioned part of a given piece and large areas 
may have wider spacing than small ones. Fig. 8, C, shows satisfactory spacing for different areas. 

34. The kinds of material used in construction have multiplied to such an extent in recent years, that 
it is no longer feasible to have a distinctive symbolical section lining for each. In Fig. 8 are shown some of the 
kinds which are in use chiefly in a pictorial way. On a working drawing these are seldom used, plain section- 
ing and definite printed specification of the material being the custom. 

35. Section lining is one of the most tedious parts of a draftsman's work. To secure uniform spacing 
on large areas, a special instrument is often used. For ordinary work, spacing by the eye is sufficiently accurate. 
Make the first few spaces carefully and then look back to them frequently for a gage on the other spaces, rather 
than at the last spaces made. For free-hand sectioning, the slant from the upper right to the lower left is the 
one to be preferred for a right handed draftsman. 

USE OF SHADE LINES. 

36. If an object is illuminated by direct light it will cast a shadow. The outline of this shadow is com- 
posed of the shadows of certain edges or lines of the object. A line which is said to cast shadow is one which 
separates a lighted surface from one that is in shade. In a projection drawing, these lines are made twice as 
heavy as the other lines and are called shade lines. The object of using shade lines on a drawing is for the 
pictorial effect only. They impart an appearance of solidity. Shade lines are now seldom used on working 
drawings, however. 

37. Light is assumed to be coming down in parallel rays over the left shoulder of the observer as he 
stands looking at the object which is supposed to be built out solid on its projection. The slant of the rays 
is such that their projections on the planes of projections have an inclination of 45°. To select the lines that cast 
or form the shadow, the pencil may be set up as a light ray, as shown in Fig. 9 P, and applied to the projection. 

In the square frame Fig. 9, A, the front surface is in the light while the surfaces at FH, GH, JK and JL 
perpendicular to the plane of the paper are in shade. 

19 



X 



.\^ 



A/^ 



Use of Shade Lines 



\ !^ 





\ 


Elevation 




£" 


\ 


F 


\ 


\ 


J X A- 

ZX M 


\ 




G 


\ 


H 





\ 




/ 


V 


F 








\ 




/ 




\ 




\ 






/ 


\ 




/ 














/ 






N 


/ 




\ 





- f 




\ 


E 








'mmmm 




o 


O 


o 




o 




o 


o 


o 




o 




o 


o 


ff/ffT- 


■YOtEJ 


UNO HEADS. 


1 1 





t 






m3 


o 



Fig 9. 



The lines mentioned, therefore separate light from dark surfaces and will be made heavy. Note that the 
shade lines on the plan of the frame have been selected as if it were an elevation. In selecting shade lines, the 
view is always treated as if it were a front view. The various drawings in Fig. 9 fully illustrate present practice 
in use of shade lines. Shade lines for cylinders, cones and spheres are selected in a conventional way as indicated. 
Theoretically, the shading of a line should be on the outside of a projection, but such a rule cannot often be 
followed. It is more frequently put on the inside of the line of the projection. At K and M are drawings of 
connected parts which show how the shading is applied to avoid notching of the lines. 

USE OF CENTER LINES. 

38. As has been pointed out in Section 13, .nearly all artificial forms have some line or lines with regard 
to which they are symmetrical. All turned forms have an axis of revolution, links such as the Rocker Arm, 
Fig. 23, have an axis line connecting centers of holes. In a steam-engine, there is the axis of the cylinder, the 
axis of the crank shaft, the axis of the connecting rod and various others. Every drilled or bored hole, every 
screw, bolt, gear and pulley has an axis. In making a drawing these lines are invariably drawn first, because 
they are very useful in making measurements. They are called center lines in the drawing and are usually 
shown as dash and dot lines. They are base lines of measurements which the workman also must use in laying 
out his work. In the Bevel Gears, Fig. 13, they are used to indicate symmetry, for dimensioning the angles 
and for distance between shafts. In the Pulley, Fig. 10, they indicate symmetry only, and this is their general 
use for isolated shafts, bolts, screws etc. While they are useful in making the drawings in this last case, they 
serve no purpose for dimensioning and for this reason are often omitted where they would seriously interfere 
with dimension figures or specifications. Note the screws in Fig. 11. 

A center line is used for the pitch line of gears as in Fig. 13, and for bolt circles as in the Cylinder Cap, 

Fig. 10. 

DIMENSIONS AND SPECIFICATIONS. 

39. It has been suggested that the projections in a drawing are important only as a suitable framework 
to which dimensions may be attached. This is an extreme view, as any draftsman who neglected his projec- 

31 



tions would quickly discover. Projections are secondary to dimensions just as the whole drawing is secondary 
to the thing it represents and just as the machine it represents is secondary to its product, and so on indefinitely. 
It is true however, that small errors in projections are frequent and sometimes permissible, though never desirable, 
while an error in a dimension may be fatal. The projection is used for illustration, while the dimension is used 
for measurement in construction. On this account, the dimensions and specifications of a drawing are its most 
important part. 

40. Three questions arise. What dimensions should be put on a drawing? Where shall they be placed? 
How are they expressed? Unless the draftsman has had actual experience with shop methods of construction, 
he will not be very successful in his selection of proper dimensions. His first inclination is to put on such dimen- 
sions as would enable the drawing to be duplicated. He must rather keep in mind the thing to be made, the 
tools the workman will use in laying out and measuring his work and the various machine operations to be per- 
formed. Constant study of approved shop drawings will give considerable information, conferences with the 
workmen will also be enlightening, but actual working on the machine in the shop is the best training for this 
part of the draftsman's work. 

The principal tools used by the shop workman are the two foot rule, steel scale, calipers, dividers, square, 
trammel points, straight edge, protractor, surface gage and other gages for threads, drills, wire etc. 

The principal machine operations are turning, boring, drilling, milling, planing, and grinding. Hand 
work such as filing, chipping and scraping should not be overlooked. 

Besides the workman's tools and machines there are other considerations. For instance, many years 
ago, the shop workman was a man of extended mechanical experience, while to-day he is more or less of a machine; 
oftentimes against his will. Instead of having an intimate knowledge of the machine he is helping to build, 
his knowledge often extends only to a part which he regularly makes. A drawing must therefore be made minute- 
ly specific and little should be left to the discretion of the workman. To this end, it is advocated that the dimen- 
sions which he will use directly should be put on the drawing, so that he need expend no intelligence in adding 
up partial dimensions. Thus in the Spiral Gear Shaft of Fig. 10, the workman in turning from the |" end to 
the If" shoulder would like a dimension equal to the sum of ||", lyV" and 43V'- Such a dimension is seldom 

22 



given by the draftsman, because he is interested only in the direct measurements which must be correct to per- 
mit fitting the piece to the parts it adjoins in the machine. If such a dimension is given, it should be in addi- 
tion to those which are direct. 

If there are finished flat surfaces on the piece, dimensions should be based on these and the same is some- 
times true regarding curved surfaces. Thus in the Pulley, Fig. lo, the thickness of the rim is based on a finished 
curved surface, but the thickness of the hub is not given by a measurement from the "bore." 

Location of parts of a piece are often made by measurement to a center line, but care should be taken 
to see that this is a satisfactory way of locating. Such a method may be desirable oftentimes for the pattern- 
maker, but might be entirely inadequate for the machinist. 

It is impossible to lay down an invariable rule for the selection of dimensions, but the following is a good 
general guide. Put on those dimensions which will be common to fitted parts and which must be exactly right; 
also as far as possible, give those dimensions which the workman will use in setting his tools to make the pattern 
or to machine the surfaces. 

41. The parts which go into machines and structures may be divided roughly into the following classes. 
Machine and hand forgings, castings, parts made in the screw machine from rod or bar stock and those numer- 
ous parts which are standard or semi-standard in form, such as bolts, keys, wire, pipe, sheet metal etc. 

Fig. 10, A 8, shows a simple forging with no machining called for except in drilling holes. If any of the 
surfaces were to be milled or planed it would be indicated by an / mark, so the blacksmith could make the part 
thicker than called for by the dimension. In machining, the part would be thinned to the stated dimension. 
Dimensions are selected as follows. For size of bar stock, |" thick and 2" wide. As all the fitting depends 
on the surfaces shown edgewise at AB, AC and BD, locations are given relative to these surfaces. Thus inside 
distance between end arms of 5|", distance from end of arm to inside of back 21", distance of ear from inside 
of end arm If". Dimensions of thickness, length and width of ear are given. Location of bolt holes is given 
from surfaces AB and BD. Specification of size and pitch of tap is given. Note that a drilled hole is 
located by its center, because it is necessary to prick punch a point on the metal to take the point of the 
drill in starting. 

23 



42. An inspection of this drawing shows that the Yoke is composed of four parts. Dimensions had to 
be provided therefore, to give the size of the different parts and to give their relative locations. This is true 
of nearly every piece used in a machine or structure. 

43. The drawing of the Pulley, Fig. 10, will illustrate the dimensions needed for a casting. As the Hoist 
Arm Yoke was dimensioned for the blacksmith and the machinist, so here the pulley must be dimensioned for 
the pattern-maker and the machinist. The pattern-maker will need diameter, face width, thickness, crown- 
ing and draft for the rim; diameter of bore, diameter, length and draft on the hub ; number of arms, section of 
arm, width and thickness of arm at rim and at hub; relative position of hub and rim and dimensions of rib at 
root of the arms. To allow for finish the surfaces to be machined are to be marked /. Note that the f is put 
on the surface where it projects as a line. 

The dimensions needed by the machinist are as follows. Diameter and length of bore, dimensions of 
key way; diameter, face width and crowning on the rim. 

The fillets or rounded corners on a casting are generally left to the discretion of the pattern-maker who 
is usually a man of intelligence. If they are of importance, however, in strengthening the casting the radius 
of each should be given. 

On small pulleys the inside diameter of the rim is often given, instead of rim thickness. 

44. The Spiral Gear Shaft, Fig. 10, illustrates dimensioning for a piece turned from round stock. Here, 
all the dimensions are for the machinist. An overall dimension tells him how long a piece of stock to cut off 
and avoids the necessity of his adding the partial dimensions. This piece is made up of cylindrical sections 
of various lengths. The diameter and length of each is given. Where a section is ground to size, the same is 
specified and it is noted that one part is ground standard, that is to exact gage, another is finished a half- 
thousandth large, while a third is ground one and one-half thousandths small. The length, diameter and pitch 
is given for each threaded part, also the kind and size of each key. No finish, as such, is specified because the 
shaft has to be machined from a much larger piece. If a large spindle or shaft were forged approximately to 
size before machining, then of course, finish marks would be used. Note also the discussion on these dimensions 
in Section 40. 

24 



'^"x /S ' Pulley 

One -C.I. Pat. No./S32 



zW^^^ ^^^T^IOD 



Sp/jral Gear Shaft 

0/V£ - fl^i^CH. Sr. y^— V. 

A2) 



: OoySTA/i. Hey 




Mark 


N/^ME 


No. 

Re<P- 


Mat. 


REMAf^HS 


A 1 


'^'.x/5''PoLL£r 


1 


C.I 


P/l t: /Vo. /S32 


AZ 


Sff^. G£^/rS^//)fr 


1 


AI.^T 


/f.BAfi. /^'O. X/J:'/.. 


A3 


CyL/NO£ftC^r 


/ 


c./. 


/^TA/o.-f-SBa 


A-^ 


C£/^rr/f Sp^/^q 


/ 


^.yy. 


iz '-/Va. /6/ilt/s. IV/^re 


AS 


<^^zy^e -3TOf 


/ 


c./. 


R^r: A/o. 79 


A6 


B/r^D£^ Hy^NOL e 


/ 


c./ 


PytTA/o. 7Sa 


A7 


f^vvc >^^ic-r 'SHOf. 


2. 


Bff. 


Pa t. /Vo. '^2S 


A3 


Ho/JT AnM YoH£ 


2 


/yj.3T 


F'0fi^.30'of3'x§" 



Fig. 10. 



45- An illustration of the dimensions necessary for a part which has been standardised commercially 
is the Cap Bolt or Tap Bolt of Fig. ii. Unless something irregular is required in the thread or head, it would 
be sufficient to give the diameter, length under head to extreme point and length of threaded part. See also 
Chapter III on Miscellaneous Details for other examples. 

46. A dimension line consists of two arrows with their shafts in the same line and their points termin- 
ating on the lines between which the measurement is taken. The measurement which is given by the figures 
is from point to point of the arrows. The following rules and suggestions give the general practice with regard 
to character and placing of dimension lines and figures. Figures 8, 10, 11 and 13 furnish illustrations. 

47. Dimensions should not be crowded on a projection nor around it to such extent as to make the read- 
ing difficult. 

48. To distinguish dimension lines from the outlines of the projection, make the former about one-half 
the width of the latter. Dimension lines are sometimes made with red ink. 

49. Make arrowheads sharp pointed and not like the heads of pick-axes. 

50. If there is not space for the dimension on the projection, it may be carried to one side by extension 
lines as in Fig. 8, C. 

51. Draw extension lines first where they are needed, then the dimension line leaving a break near its 
middle (or at one side when necessary) for the figures. Put on arrow heads next and figures last. 

52. If the space for the dimension is very limited use one of the methods shown in Fig. 8, C. 

53. Extension lines should not quite touch the lines they extend. 

54. Extension lines should be of the same weight as dimension lines. 

55. A dimension line must never coincide with a line of the projection. 

56. A dimension line must never coincide with a center line. 

26 



57- When the dimension Hne gives the radius of an arc, use an arrowhead at the arc end only. See 
Friction Pawl Shoe in Fig. lo. . 

58. When several dimensions are parallel, the longest is placed furthest out to avoid confusion of exten- 
sion and dimension lines. 'See Cylinder Cap, Fig. 10. 

59. Dimension lines for an angle are usually circular arcs with centers at the vertex of the angle. See 
Fig- 13- 

60. Dimension figures give the actual size of the measurement indicated, although the drawing may 
be much smaller than full size. See Pulley, Fig. 10. 

61. Dimension figures should read with the line and from the bottom or right end of the sheet for hori- 
zontal and vertical dimensions. For oblique dimensions, practice varies, but many draftsmen put all such 
figures horizontal. 

62. Figures must be large enough to be perfectly legible in the blue print which is often made from the 
drawing. They should be very carefully formed. If space is too limited, take the figui'es to one side with an 
arrow to indicate where they belong. 

63. The division mark for fractions should be parallel to or in line with the dimension line. 

64. Many draftsmen specify all measurements up to 24" in inches and those above 24" in feet and inches. 
Practice is quite variable in this matter and diameters of turned forms especially are often given in inches even 
though of very large dimensions. Thus, a 32" shaft, a 72" pulley, a 54" cylinder. 

65. If all the dimensions on a sheet are in inches, the inch mark on figures is often omitted. 

66. If some dimensions are in feet and inches, then the foot and inch marks should be used and the 
figures separated by a dash. Thus, 2'-7", 3'-0", 7ft. -5". 

67. If the size of a fillet or rounded corner is of importance, its radius should be given as in the Pulley, 
Fig. 10, the figures being followed by the letter R or by Rad. 

27 



68. If the whole of a dimension hne is not shown, some specification must be added to explain its extent. 
Thus in the Pulley, Fig. lo, the figures for the diameter are followed by DIAM. 

69. If the size of a part is changed after the drawing is completed, it is customary to change the dimen- 
sion figures, but not the projection. For instance, suppose the hub diameter of the Worm Gear in Fig. 13 were 
changed to IV'. Cross, but do not erase the 1{" and specify below, "changed to 1^'. " 

70. Dimensions for angles may be specified by the number of degrees and tenths or by the amount 
of vertical rise on a given length of horizontal base. The former should be used where the measurement is to 
be made with a protractor, the latter is generally more convenient for the pattern-maker and is always used 
in structural work. See Fig. 13. 

71. Dimension figures must never on any account be crossed by a line, nor placed so as to interrupt 
a line of the projection, nor an extension line. Note also the break in section lining about figures and lettering. 
See Figures 10 and 13. 

72. Give diameters of circles and the radius of a circular arc less than a semi-circle. If the location of 
the center of a circle or arc is not indicated by lines of the drawing it should be definitely located and dimen- 
sioned. 

73. Do not duplicate a dimension given in another view, except for purposes of identification of a part 
otherwise not easily distinguished. 

74. Dimensions should be placed where they will be found quickly by the workman. They can gener- 
ally be arranged in natural groups and should be put on one view as much as possible. Thus in the Pulley, 
Fig. 10, all the hub and bore dimensions form a group and are on the same view. The key way dimensions are 
shown in the view where all can be put on. For the lengthwise partial dimensions on the Spiral Gear Shaft, 
Fig. 10, an arrangement very nearly in a straight line is desirable. 

75. Supplementary to the dimensions is the printed matter that accompanies the drawing. The name 
of the piece, usually some identification number or symbol, the nmnber of pieces reciuired for one machine or 

28 



structure, the material, the kind and extent of finish, heat treatment such as tempering and any other pertinent 
and necessary facts are grouped together above or below the drawing to form a sub-title. See Figures lo and 13. 

76. Notes are also added to explain special details and these should be exactly definite. See notes on 
Bevel Gears and Spiral Gears Fig. 13. 

77. Specifications for much material that is used is given by gage size or by nominal size and these are 
as follows: 

Belting. Leather belts; give width in inches and number of thicknesses. 
Chain. Give diameter of rod used for link. 
Drilled holes of small size. Give Drill Gage number. 
Machine Screws. Give diameter by Screw Gage. 
Pipe. Wrought Iron Pipe; give nominal inside diameter. 
Pulleys. Give diameter and face in inches. 
Rope. Give largest diameter. 

Shafting for transmission purposes is specified bj' its nominal diameter. Thus a 2" shaft measures Ijf " 
diameter. 

Sheet Metal. Thickness is given by gage or in thousandths of an inch. 
■ Tubing. Give outside diameter and Gage thickness. 

Wire. Give diameter by Wire Gage or in thousandths of an inch. 
Wire Cloth. Give number of meshes per lineal inch and Gage of wire. 
Wood Screws. Give diameter by Screw Gage. 

78. Drive, force and shrink fits should always be specified. 

79. If a piece is hardened, tempered, case hardened, blued, nickled or ox3alized it should be noted. 

80. Specifications are often made bj^ giving name of manufactm-er or the trade name or number bj' 
which he designates a machine or part. Thus, No. 825 Ley Bushed Chain. 

29 



8i. Specifications for the common forms of fastenings, such as are shown in Fig. ii, are given in 
Chapter III. ' ' 

LINES OF THE DRAWING. 

82. The various lines used in working drawings are shown in Figures 8 to 13 inclusive. General practice 
is to make all lines with black ink. There are three features to be considered in determining the character of 
these lines. 

They should be easily distinguished from each other in the original drawing and in the blue print, and 
should not consume too much time in the making. 

83. The visible lines of the object are shown by continuous or full lines not less than gV in width for 
ordinary drawings. 

Hidden lines of the object are represented by dotted lines not less than g\" in width. The length of 
dot will vary with the size of the drawing and length of the line. The space between dots or dashes should be 
just long enough to show that the line is broken. The end dot should start at the full line, provided it does 
not thereby become a continuation of some other line. Otherwise, start the dotted line with a space. See 
dotted lines in Bevel Gears, Fig. 13. 

Center lines may be full lines or of alternating dots and dashes. In either case they should not exceed 
J the width of lines of the projection. 

Extension lines may be full lines or dash lines and of the same weight as center lines. They must not 
quite touch the lines they extend. 

Dimension lines are usually made as two long dashes with a break for the dimension figures. For long 
lines they may be long dashes. Width of line should be same as for center lines. 

Shade lines should be twice the width of the lines of the projection. . 

Other lines may be combinations of dot and dash lines. 

30 



GENERAL ARRANGEMENT OF A SHEET 

84. The general arrangement of a sheet of details will be similar to that of Fig. 10 but not so crowded. 
Each part with its projections, specifications, dimensions and sub-title should constitute a group somewhat 
separated from the others, so as to be easily picked out by the eye. 

85. The title of a sheet, described in Section 245, will usually be placed in the lower right hand corner. 
It will provide a variety of information according to the system in use. 

86. Near the title is often placed a Bill of Material similar to that in Fig. 10. It is to facilitate the work 
of order and cost clerks. Many prefer a different order by which the number of pieces required is given first 
and the name of the piece second. 

87. There are usually placed at the lower right and upper left hand corners numbers or symbols to des- 
ignate the sheet and its contents for convenience in filing, indexing and reference. 

CHAPTER III 

MISCELLANEOUS DETAILS OF CONSTRUCTION 

88. Many of the simpler parts used in construction are common to all or most machines and structures. 
These will be considered at some length in the order of their arrangement in Figures 8, 10, 11, 13 and 14. 

TYPES OF SCREW THREADS FIG. 11 

89. The Sharp Vee is used to only a limited extent, as it is difficult to keep taps and dies for it in con- 
dition. The sharp edge of the V wears down and approaches the shape of the U. S. Standard Section. Its 
lack of clearance makes it difficult to fit, if cut in the lathe. 

90. The Sellers or U. S. Standard is like the Sharp Vee with the point of the triangle flattened | of the 
height, at top and bottom. This is the thread in common use in the United States. 

31 



Qi. The International Standard adopted by the metr'c countries is not shown here. It is exactly the 
same shape as the SeUers thread except that the point of the V at the bottom of the thread is rounded yV of 
the height. This is an improvement over the Sellers section, in that it provides clearance and facilitates fitting. 

92. The Whitworth, or English standard, has an angle of 55° and the point of the V is rounded top and 
bottom ^ of the height. 

.93. The Buttress thread gives a form of great strength where the load is always in the same direction. 
Its friction is low and it is easily fitted. It finds application in Bench Vises and Screw Jacks. 

94. The U. S. Buttress is a modified form of the preceding used by the U. S. Government for breech 
blocks of guns and for armor plate bolts. 

95. The Square thread is used for power transmission screws where large pressures are applied. Its 
friction is low, but it is expensive to fit. 

96. The Acme thread is used for screws like the lead screw on a lathe. It has some of the good qualities 
of both the U. S. Standard and the Square threads. It is often called the Powell thread. 

97. The Knuckle thread is useful where a thread is liable to be bruised, as it will stand many knocks 
and yet work in its nut. 

CONVENTIONAL SCREWS FIG. 11 

98. The true curve of the edge of a screw thread is a helix and this, of course, cannot be drawn every 
time a thread is represented. Various conventional representations are therefore used which show the thread 
with more or less accuracy and save the draftsman's time. Those shown at A, B, and C are the ones commonly 
used. The thread lines are drawn at a slight inclination approximately that of the actual thread of the same pitch. 
The spacing is also approximately true. Note that the short lines are made heavier. At C is a form, useful 
where the space will not permit the intermediate lines. 

99. In the Vee R. H. Single screw, the thread makes eight complete turns or wraps about the cylinder 
in one inch. It is therefore called a No. 8 thread or an 8 Pitch Thread. The linear pitch of the thread is really 

3^ 



rypE6 OF 6c/^£:w Threads Conventional Sche\a/3 

Sharp Vee Sellers or U.S. stano. Vee-R.H.-S/n^le. Square Double 



Conventional Threaded Holes 

A B C D E F 




Fig. n. 



J", or the distance between centers of two adjacent Vees. In the Sq. L. H. Sing, screw, is shown a thread in 
which the hnear pitch is j". There are four wraps in one inch and it s called a 4 Pitch thread. 

100. In the Square Double screw, two distinct threads are wound on the cylinder, as indicated. Each 
wraps around the cylinder twice in one inch and each is really a 2 Pitch thread. The distance between adjoin- 
ing threads, however, is only I", so to avoid confusion, it is customary in the case of multiple threads to use 
the actual linear pitch of the thread or helix and designate it lead. So in this case, we have J" lead. 

1 01. However elaborately a screw is drawn, the pitch should be specified always. If it be irregular 
in any way, that is, if it be multiple threaded, or left handed, it should be so designated. 

CONVENTIONAL THREADED HOLES FIG. ii 

102. Here we have various ways of showing threaded holes, so as to save time and avoid the confusion 
of lines. A and D are not much used. Note the angle of 120° used to show the drill point. Note also that 
the depth of the hole is not measured to the drill point, but to the corner. If two parts are threaded together 
and then cut with a sectioning plane, it is necessary to draw the thread. See Fig. 8, B. 

COMMON FORMS OF BOLTS FIG. ii 

103. Through Bolts are always used where possible, in order to reduce expense. In some cases, however, 
as on a steam engine cylinder end, it may not be possible to get at the head of a bolt on the back of the cylinder 
flange. In such a case, stud bolts would be used for holding on the cylinder head. A tap bolt is sometimes 
used for the same purpose, if the cylinder head will not be removed very often. Where a bolt of this kind is 
frequently turned in and out of a hole tapped in cast iron, the thread on the hole is quickly destroyed. Such 
a bolt is therefore most suitable for a permanent connection. 

104. The anchor bolt for concrete is to be placed while the concrete is yet plastic. The one for stone 
is driven into a hole that flares slightly at the bottom, the wedge spreading the end to fit it. 

105. If one view of a bolt head or nut is shown and then only for pictorial purposes, the hexagonal form 
should show three faces and the square form should show one face. There can then be no question as to which 

34 



is intended. If one view only is shown in a working drawing, show two faces for the hexagonal form and one 
for the square. This permits dimensioning the distance between flats, a measurement the workman will need, 
if the faces are milled. 

io6. The needed dimensions on the stud bolt are shown. Nut and bolt dimensions follow no universal 
standard. They are most frequently made by the U. S. standard, the proportions for which are given in the 
drawing. These values apply to both square and hexagonal forms. Note the appearance of the champfer 
on head and nut. Its angle is 45°. Note also that the bolt points are either rounded or beveled at 45° and that 
the thread lines do not run to the extreme point. The length of a bolt is measured from under its head to its 
extreme point. The diameter and length of thread are also essential dimensions. Pitch of thread need not 
be specified on a through bolt, but it is necessary on a tap or stud bolt, so as to agree with the tapped hole into 
which it will go. 

SCREWS AND SCRE\V HEADS FIG. ii 

107. The terms "bolt" and "screw" are used interchangeably by so many people that it is difficult 
to distinguish between them. We may classify them roughly by saying that a bolt is a screw and a nut, while 
a screw is simply the one piece. 

The ways of representing and dimensioning the commoner kinds of screws are shown here. For the Collar, 
Knurled, Fillister and Button head screws, the length is measured from under the head to extreme point. For 
the Flat head, however, it is the overall length which is taken. Most bolts and screws pull the parts they con- 
nect together. A Set screw acts by forcing them apart. For this reason it has to be case hardened, at least 
on the point. 

Many screws are turned out of bar stock and their diameters run on the common fractional sizes. They 
are called milled screws. Small screws are made from wire by upsetting one end for the head. Their diameters are 
therefore the wire sizes and are specified by the numbers of the screw gage. These are designated machine screws. 

108. Punched washers are designated by the largest size of bolt with which they can be used, and their 
thickness by sheet metal gage. Cast iron washers are regularly dimensioned. 

35 



lOQ. A lag or coach screw is a large wood screw made to be driven by a wrench instead of a screw driver. 
Necessary dimensions are as shown. 

RIVET FASTENINGS FIG. ii 

no. There is a great variety of rivet forms and only the three common ones are shown. Length and 
diameter as indicated designate the size. Note how the length of the comitersunk head type is measured. Pro- 
portions of heads vary, but are approximately as shown in the illustration. 

111. Conventional Rivet Signs enable the draftsman to avoid crowding his drawing with printed notes 
regarding the heads and points of rivets. They also permit a great saving of his time. 

112. Structural steel shapes are designated in the following way. 

For an I Beam give the depth of web and number of pounds weight per foot. 

For a Channel give the depth of web and weight per foot. 

For an Angle give the dimension of the long leg, the dimension of the short leg and the thickness in the 
order stated. 

For a Z Bar give the depth of web, length of leg and thickness in the order stated. 

For a T Bar give the width of flange, the depth of bar along the stem and the weight per foot in the 
order stated. The drawings show the way in which the specification is made. 

113. The center line of a row of rivets is called the working line. 

The working lines for rivet holes on structural shapes are called gage lines. 

The center line for a row of rivets is located relative to a finished edge of the plate and the last rivet of 
the row is located from the end of the plate. For structural shapes, the holes are located as shown in the drawings. 

KEY FASTENINGS FIG. ii 

114. There are three types of keys in common use as follows. A Taper key, such as is used for fasten- 
ing a pulley to a shaft so it cannot rotate nor slide on the shaft, fits on all sides and is driven in tight. If its 
small end is not accessible for driving out, then a Gib-Head key is used like the one shown in the drawing. The 

36 



section under the head is commonly square. This dimension and the length under the head are sufficient to 
designate it. 

115. The second type of key fits on the sides and prevents relative rotation but not sliding endwise. 
These keys are commonly square and are dimensioned as in the drawing. The Woodruff key, designated by 
number or by length and width, belongs to this class. 

116. The third form of key is the Feather key. This is usually rigidly attached to the shaft or to the 
hub, so as to permit sliding of the parts endwise without its loosening. These keys are generally of greater 
depth than the other kinds. The depth or thickness of a key is its radial dimension as it lies on the shaft. 

117. A key tends to fail by shearing on a longitudinal section. A Cotter is a similar fastening which 
tends to fail by shearing crosswise. Cotters are often called keys especially on the connecting rod of an engine 
where they are used to draw up the boxes. A cotter is tapered and is driven tight to draw the connected parts 
together. It may hold by friction or be held by a set screw. In specifying, use the dimensions shown in the drawing. 

118. A spring cotter or split pin is not used for drawing parts together, but to prevent a pulley or nut 
from coming off a shaft endwise. After pushing the pin through its hole, the ends are spread thus preventing 
its working out. Diameter at the neck and length under head to extreme point are the necessary dimensions. 



AODtNDUM UlNE 




Fig. 12. 

line is the addendum and the part inside, the dedendum 
37 



TOOTHED GEARS FIG. 13 

119. If two cylinders revolving on parallel shafts are pressed together, 
one will drive the other by friction, if the resistance of the driven cylinder to 
turning is not too great. With great resistance, slipping will occur and to 
avoid this, projections may be put on each cylinder with hollows between to 
accommodate the projections of the other. If these projections and hollows 
are properly shaped, the result is a pair of toothed gears. The original 
cylinders are called pitch cylinders. In Fig. 12, the pitch line or. pitch circle 
is the projection of the pitch cylinder. The part of the tooth outside this 

The length of pitch line between centers of two 



adjacent teeth measured in inches is called the circular pitch. The tooth width is measured in the same way 
on the pitch line, as is also the space width. Note also the fillet and the clearance. The working depth 
line shows how near; the tops of teeth of a mating gear approach-to the bottom of the space. Face of a tooth 
is the working surface outside the pitch line and the flank is the working surface inside. 

120. Ordinary gears have a whole number of equal teeth and of equal spaces. If the number of teeth 
on a gear be divided by the diameter of the pitch circle in inches, the quotient is a number called the diametral 
pitch. Thus in the Spur gear Fig. 13, 16, the number of teeth, divided by 2, the number of inches in the diameter 
of the pitch circle, gives 8, the number of the diametral pitch. This diametral pitch is the one commonly used 
in designating the gear. It is useful to remember that Circular Pitch X Diametral Pitch = 7r. 

121. For cut teeth the proportions are as follows. 

Tooth Width = Space Width = J Circular Pitch. 

1 • 

Addendum Length =^j^^^-^:^^p^ 

Addendum Length, Tooth Width 
Clearance = ^ or Clearance = r- 

Dedendum = Addendum + Clearance. 
Fillet Radius = Clearance. 

In the case of Cast teeth not machined, the space width exceeds the tooth width by an amount called 
the back-lash. This provides for running in spite of irregularities of the teeth. 

122. Tooth outlines are single curved or Involute, as in the Worm Gear, Fig. 13, and double curved or 
Cycloidal as in Fig. 12. 

123. The dimensions needed on the drawing of any gear are as follows. Dimensions for the pattern- 
maker, if a casting is used; dimensions to enable the machinist to turn up the blank, as the uncut gear is called, 
and dimensions necessary for selecting the cutter and setting up the work in the machine where the teeth are 

38 



cut. Only those dimensions and specifications relating directly to the teeth will be mentioned in considering the 
following gears. 

SPUR GEAR FIG. 13 

124. Dimensions necessary for teeth are thickness and outside diameter of blank, number, kind and 
l^itch of teeth. 

RACK FIG. 13 - 

125. A rack is essentially a Spur Gear with an infinite diameter. Give its length and width, the kind 
and pitch of teeth. 

WORM GEARING FIG. 13 

126. If the teeth on a spur gear are turned slightly so their angle agrees with the thread angle of a screw 
having the same circular or linear pitch, the two will work together properly and constitute a simple form of 
Worm Gearing. The thread section of the worm is made like a rack tooth and the relative action of the teeth 
can be best understood by thinking of the worm as a rack. 

If a more extended contact between the thread of the worm and the teeth of the gear is desired, a mill- 
ing cutter is made which is almost an exact duplicate of the worm. This is run with the worm gear and shapes 
its teeth. Such a cutter is called a hob and when one is used, the teeth of the gear are often first roughed out 
with a rotary cutter set at an angle to agree with the thread angle. This operation is called gashing. 

All the dimensions relating to the tooth are calculated with the exception of the outside diameter of the 
gear, which is measured from the drawing. Dimensions should be given in thousandths of an inch. 

Dimensions for Worm are, length, outside diameter, root diameter, lead and kind of meshing tooth. If 
more than one thread is used it should be specified. 

Dimensions for Worm Gear are, outside diameter, width and bevel of blank; throat diameter, radius and 
width of groove; number, kind and circular pitch of teeth; tooth angle should be given if the gear is gashed. 
Tooth dimensions are based on the fractional diametral pitch corrcspond.ng to the given circular pitch and in the 

usual way. The addendum length in these teeth is equal to — or .07958". 
39 



Spur Gejar 



Rack 



0/V£ - CJ. - f y^LL OK£-/i -/S°//\iyOL. OA/£-C./.-f ALL Oi^£f^ -/2P/-STD. CyCL. 



Bei/el Gears 
One Each - Mach. Qt. 



90 

60°.2i, 

26?9i 



E - Shaft A/^0LE 
F- Center Anqle 

H- FACE ANGiLE 

J - Angle of edge 

L ~ Cutting Angle 

^M- BACHING 

D 

Pjtch Cones 

ABD -BCD 



I ■3." 

'/e 




BEVEL GEARS FIG. 13 

127. In bevel gears the pitch surfaces are cones. In the cb'awing they are showni as isosceles triangles 
DAB and DBC. The pitch circle on the pitch cone, used for calculations is AB for the small gear and BC for 
the large, that is, the largest in each. 

Considering now the small gear only, note that a tooth tapers from its large end as at UAT toward the 
vertex, D of the pitch cone. The dimensions of the large end of the tooth are the ones used in calculations and 
it should be observed that this large end lies in the surface of a secondary cone whose elements are perpendicular 
to those of the pitch cone. This cone VAB is called the back ccne. The pitch diameter of the small gear is its 
largest pitch diameter i. e. 2". The number of teeth is 20 and the diametral pitch is therefore number 10. The 
tooth addendum length AT is yo" and the dedendum length AU is ^q". The various angles and increments 
may be computed by trigonometrj^, or by means of Bevel Gear Tables. 

Thus, having the pitch radii of the two gears, BZ and DZ, the center angle of 29°.7.5 can be found. AD 
can be found as the h3q3othenuse of the triangle AZD. From AT and AD, find by trigonometry the angle ADT, 
which added to the center angle gives 32°. 58. The complement of this angle, 57°.42 is the face angle. From 
UA and AD determine angle ADU, which subtracted from the center angle gives 26°. .55 for the cutting angle. 
The angle VAZ is called the angle of the edge and it is equal to the center angle. The outside diameter equals 
pitch diameter AB, + 2 AT Cos. 29°. 75. The cutter is selected for 10 pitch and for a number of teeth equal 

AV 

to the number of teeth of the gear, 20, multiplied by — . 

AZ 

To size for teeth, the machinist will need the outside diameter, the backing, angle of the edge, face angle, 
face of blank. For cutting teeth, he will need the number, kind and pitch of teeth, the number of teeth which 
determines the cutter and the cutting angle. 

SPIRAL GEARS FIG. 13 

128. If instead of a single thread on the worm used with the worm gear, a large number of threads had 
been used, then the lead would have been greatly increased and the angle between the tlii'ead and the axis of 

41 



the worm as shown in the projection would have greatly decreased. The threads on the worm would then appear 
more like teeth than threads. The tooth angle on the worm gear would have changed accordingly and the result 
would be two similar gears in which the teeth were portions of threads of very large lead. Such gears are called 
Spiral Gears. 

In the case illustrated by the drawing, the center distance between shafts is 4^|", the ratio of numbers 
of teeth on the gears is f, the shaft diameters are IJ" and cutters to be used in cutting the teeth are 6 pit-ch. 
These are all fixed conditions and there would be many solutions that would satisfy them. The solution will 
not be outlined here, as it requires extended explanation. The necessary dimensions are shown in the drawing. 
Note that the relation between pitch diameter, pitc-h and number of teeth is not as in other gears. 

129. The pitch diameter is always given on a gear although it may be of no use to the machinist. *It 
is necessary, however, in determining the center distance between the connected shafts, or for checking and com- 
puting parts of the gear. For gears with cast teeth, it is needed by the pattern-maker in laying out and setting 
teeth. 

The machinist, in cutting teeth, needs many dimensions not given, such as total depth of cut, addendum 
length etc., but these are seldom put on a drawing of the nature here described. 

130. Spur gears are used to connect parallel shafts. Bevel gears to connect shafts not parallel, but in 
the same plane. Spiral gears are used to connect shafts not in the same plane and at any angle. Worm gear- 
ing to connect shafts not in the same plane, but at 90° angle. Bevel gears of the same size connecting shafts 
at 90° are called Mitre Gears. 

-r , ,, , .^ ^. /• .1 • 1 turns per minute of the driver , 

In each case the velocity ratio or the pair equals, . ^ equals 

turns per minute of the driven 

number of teeth on the driven txi c • xui 111 xi ± ^^ 
. . In the case ot worm gearing, a thread would be counted as one tooth. 

number of teeth on the driver 

131. Note the dimensions and specifications for the coiled spring in Fig. 10. 

42 



PIPE CONNECTIONS FIG. 14 

132. Ordinary Standard wrought iron pipe is designated by its nominal inside diameter. Thus a 12" 
pipe is just 12" in internal diameter, while a |" pipe is .269" in internal diameter. 

Extra and Double Extra pipe are of the same outside diameter as Standard, so their inside diameters 
have no significance. The thread for a pipe is special, standard for the various sizes and is never specified in a 
drawing. If a hole is tapped for pipe the specification is, 2" Pipe Tap, for instance. 

133. The term fittings applies primarily to the parts used for connecting the different sections of pipe. 
Valves are not considered fittings. Sketches of the various fittings and their names are given in Fig. 14. Their 
use is explained in the sketch showing a pipe "layout." 

The size of a fitting or valve is given as that of the largest piece of pipe which can be screwed into it. 

A straight coupling connects two pipes of the same diameter, while a reducing coupling connects two 
pipes of different diameters. Many fittings are threaded right and left to permit of making connections on a 
circuit of piping. If the connection must be sometimes broken, it is better to use unions to complete the 
circuit. 

Elbows and bends provide for changes in direction, while Tees, Crosses and Y branches provide for branches 
and for changes of direction. 

On a fitting with side outlets the main part is called the run. The fitting is always specified by giving 
first the dimensions of the run and then those of the outlets. In Fig. 14, Y, is shown how to designate a Tee. 

A flange union is used where the joint must be tight and the pressures are high, as on steam piping. Screw 
unions are used on the smaller sizes of pipe, especially for water pipe. 

134. The conventional drawing of a pipfi "layout" shown in Fig. 14 may be further simplified by using 
single lines for the pipe and fittings. A riser is a vertical section of pipe. In a sketch of this kir.d, give dis- 
tances to center lines of pipe, the size of pipe, name and size of each fitting, kind and size of each valve, cock, 
drip, lubricator or other apparatus on the line. For an inclined pipe, give the vertical rise in a given horizontal 
distance. 

43 



STffA/QHT Cou/'i.INq /^EDUCW^ COUf^ 



Y B/iANCH 



4-5" Elbow 



— yw*'^»'iA 



( 
I 

1 
I 
I 
I 



Close Fetu/^n Bend 





Beaded F/rr/NQ 




Railing FirriNq 



m 

A 
L 
5 



Flange^d F/T TINQ 

rrJ/'//l/A 



'<V /// f'A 



Sewer 
Pipe 





For Rapid Conventional Sketching 



This is a Plan View 



(^ 



Cap op Pi.oQ\^^ J 



\i' 



Run 



Y 



IIS ^^^^ """-J^ 

m 



loit 



/iXl'X^ TEE 




Fig. 14. 



TAPERED PARTS 

135. Tapered arms and hubs of pulleys, sheaves, gears and other wheels are designed for a certain amount 
of total taper per foot. This taper is usually given on a drawing, however, by specifying the dimensions at the 
small and large ends. See Pulley Fig. 10. 

Tapering arms of levers and handles are designated in the same way. See Binder Handle, Fig. 10. 

Tapered parts that fit tapered openings are usually specified by giving the dimension at one end and the 
taper in inches per foot. See Gib Head Key and Cotter in Fig. 11. 

Taper of centers, tool shanks and pins is designated by giving the diameter of the small end and the taper 
in inches per foot as measured on the diameter. See Fig. 8, B. 

A tapered hole is drilled, turned or bored and reamed. The drill diameter, taper in inches per foot and 
diameter at the large end are to be given. If some one of the numerous standard taper reamers is used, it should 
be specified. Thus, No. 3 Morse Taper. 

On account of the confusion regarding the measurement of tapers, many draftsmen prefer to make a sup- 
plementary construction showing just how the taper is measured. 

REFERENCE BOOKS ON GEARING 

136. Essentials of Gearing — G. C. Anthony. 
A Treatise on Gear Wheels — G. B. Grant. 

Practical Treatise on Gearing — Brown & Sharpe Mfg. Co. 
Formulas in Gearing — Brown & Sharpe Mfg., Co. 
Worm and Spiral Gearing — F. A. Halsey. 



45 



CHAPTER IV 

GENERAL SUGGESTIONS ON TECHNICAL SKETCHING 

137. In instrumental drawing exact measurements are made, but in free-hand work measurements 
are approximated by the eye and must be largely relative. Dependence on instruments will usually hamper 
the free-hand draftsman and a sketch that is partly free-hand and partly mechanical is unsatisfactory. It requires 
but little practice to draw free-hand lines that are fairly straight or parallel and irregular curves are drawn quite 
as easily as with instruments. A free-hand sketch, if not too complicated, can often be drawn in a quarter the 
time required for an instrumental drawing and an expert will often make a sketch before the other man can set 
his compasses. 

138. Some students draw with a pencil in one hand and an eraser in the other. It is interesting to watch 
them. They will draw half an inch of a line and immediately erase it, because of real or fancied error. This 
is entirely wrong. If the line looks wrong, leave it alone and draw another beside it, across it, or any way so 
it looks right. If this is wrong, let it stand and draw others. An ellipse thus drawn may look like a bird's nest, 
but the true line can be picked out of the collection, made heavier and the others erased. 

Inspection of sketches made by masters will show all this jumble of trial lines which they did not consider 
of enough importance to erase. 

139. Practice at the blackboard where a free arm motion cannot be prevented is good training. In 
drawing a straight line, think of the point to which the line is going rather than about the hand or pencil. Curves 
may be sketched in, by first spotting a few points in them. 

140. To get fair proportions in a drawing, both the relative length and the angularity of the straight 
lines must be carefully considered. To get proper lengths, let some line of the object be taken as a unit and 
compare all other lengths with it. Then check by comparison of various related lines. To make these compari- 
sons with celerity, the draftsman should become familiar with the appearance of different fractional divisions 
of a line. Measurement in eighths is a familiar and useful one as they are easily obtained by continued halving. 

46 



See line AB in Fig. 15. Thirds, sixths and fifths are also useful. To get thirds, place the pencil at 1 on CD and 

some other marker at 2; then adjust until the divisions look equal. Sixths are 

obtained from thirds by halving. For fifths use two markers as at 3 and 4 on EF 

and adjust until the distance between them is half of each end space. Sevenths are 

obtained on GH in a similar way, the markers being adjusted till the distance, 5-6, 

between them is two-thirds of the left end space and equal to the right end space. 

141. Inclination of a line is generally approximated by comparison with a 
horizontal; sometimes with a vertical if more convenient. The eye can detect a 
small error in a right angle and in parallel lines, but for intermediate angles a large ^'s- ^^■ 

error will often pass unnoticed. Great care should therefore be taken with perpendiculars and parallels. 





— 1 — 

4- 


r 

a 


h 1 

/ 

/ 

1 


s i y P 

z 

1 ,n 


Fs 






J 


4- 
1 , ,f 


G^ 


7 
— L— 




s 

\ 


6 

\ H 



Foff £srmAT/N<s 

Angles 
60" 




Fig. 16. 



142. For estimating angles intermediate between 0° and 90°, we naturally 
halve the quadrant getting 45°. This is always readily tested, because it is a rise 
of one on a base of one as shown in Fig. 16. Another angle familiar to most drafts- 
men is the 30°. This can be tested by the fact that the short leg F-30 of the right 
triangle is one-half the hypothenuse B-30. By halving the 30° angle we get the 
15°. Another familiar angle is the 60°. Here, the base BD is half the hypothenuse 
B-60. By halving the angle between 60° and 90° we get the 75° angle. All these 
angles are in frequent use in engineering work and the student should become 
familiar with their appearance. With the quadrant divided thus into six equal 
parts intermediate angles may be approximated with considerable accuracy. 



143. If the plane of a square is parallel to the plane of projection or to the picture plane, the corner angles 
will appear as right angles and the diagonals will bisect them in the drawing just as in the original. If the square 
is placed so all its edges are oblique to the plane of projection or to the picture plane, its projection will be a par- 
allelogram and its perspective a trapezium. The corner angles of these figures are not right angles and their 
diagonals do not bisect the corner angles. See Fig. 28, B, and Fig. 3, A. 

47 



144- If the square is placed so one side is parallel to the plane of projection or to the picture plane, then 
the projection will be a rectangle and the perspective very nerrly so. 

145. If an angle be placed so its bisector is parallel to one of the planes of projection, then the pro- 
jection of the angle on that plane, will be bisected by the projection of the bisector. 

146. It is therefore very important to remember, that in constructing figures whose planes are not par- 
allel to the plane of projection nor to the picture plane, no use can be made of the actual angle between adjacent 



edges. 



sides. 



147. A triangle should be constructed by drawing its base, its altitude, its vertex and last the oblique 
To locate the altitude properly, note how it divides the base line. 

148. In the equilateral triangle, Fig. 17, the altitude bisects the base. Note that 
the altitude is approximately equal to | of the base. The vertices of the concentric triangle 
are on the altitude lines. To construct the triangle draw BC, mark its middle point D, 
draw AD, locate A and draw AB and AC. This completes ABC. To construct FGH, 
measure off DE as a fractional part of AD, draw FG parallel to BC, draw altitude CK 
and BL, locate F and G and draw FH and GH parallel to AB and AC. Or FH and GH 
may be located in the same way as FG, if the preceding con- 
struction gives poor results. 




AD=DC= CE^EB=±AB 
rj- .G 



149. In the regular hexagon, Fig. 18, the short diame- 
ter, FH, is approximately | of the long diameter, AB. A side 
is equal to \ AB and the lines FH and GJ bisect AC and CB. The vertices of the 
concentric hexagon are on the diagonals of the outer figure. 

To draw the outer hexagon, draw AB, halve it, quarter it and draw FDH 
and GEJ. Locate F and H, draw FG and HJ parallel to AB. Draw last AF, AH, 
BG and BJ, then check by noting if opposite sides are parallel and. equal to one-half 
their parallel diagonal. The base of the nut in Fig. 32, K, was drawn in this way. 




Fig. 18. 



48 



150. Rectangular figures are constructed without difficulty by drawing their sides directly. Their 
diagonals intersect at the center. 

151. After the rectangle, the circle is the commonest figure with which the draftsman has to deal. If 
it is remembered, that it can be inscribed in a scjuare, it will be easier to draw, 
whether it is shown as a true circle or as an ellipse. 

In Fig. 19 a circle is shown inscribed in a sqviare. It touches the sides at the 
middle points. It cuts the diagonals at a distance from the center equal approxi- 
mately to -^ of the half diagonal. To draw the circle, mark its center and spot 
four points as E, F, G, and H equidistant from it. These points are needed not so 
much to produce a good curve as to insure its proper location and size. For the 
--^^ concentric circle, similar points may be taken, the distance between the two curves 
being measured on a radius and as a fraction of the large radius. Thus in the 




figure this distance is 4 of the large radius 



152. Suppose a circle is placed so its plane is oblique to the plane of projection, or to the picture plane. 
It may be proved that its projection, or its perspective is an ellipse. The circle has an infinite number of diam- 
eters and one of them will be parallel to the plane of projection and project in its true length. This will be the 
longest diameter of the ellipse, or its major axis. In the same way, one of the diameters will project shorter 
than any of the others and this will be the shortest diameter, or minor axis of the ellipse. These two axes are 
perpendicular in the ellipse and the curve is symmetrical with respect to each. 



153. 

the first. 



The projection of the concentric circle 
For instance if the radius of 



will 



an ellipse 



the second circle is f that of the first 



similar to 
then 



each radius of the inner ellipse will be f of -the coincident radius of the outer ellipse. 
This is shown in the full lines of Fig. 20. Thus ON=f OF and OP = f OQ. 




Fig. 20. 



154. Returning to the circle described in Section 152, suppose a line be drawn 
perpendicular to the plane of the circle at its center. This line will be perpendicular to every diameter of the 



49 



circle, therefore perpendicular to that one which is parallel to the plane of projection and which projects as the 
major axis of the ellipse. By the principle stated in Section 144, the projection of the line perpendicular to the 
plane of the circle will be a line perpendicular to the major axis of the ellipse. 

This is one of the most important principles relating to the projections or perspectives of cylindrical forms 
and its common violation, through ignorance, results in disagreeable distortions. 

From this principle, it follows that a circle whose plane is horizontal will be represented by an ellipse 
whose major axis is horizontal. 

155. The principles enunciated in Sections 151, 152 and 154 apply to correct perspective drawings as 
well as to projections. In the case of concentric circles the perspective representation is slightly different . The 
inner circle is shown as an ellipse, but its center does not coincide with that of the outer ellipse. This is shown 
by the dotted lines in Fig. 20. The plane of the circle is below the eye. 

156. A square circumscribed about the circle of Section 152 will project as a parallelogram. The ellipse, 
the projection of the circle, will touch the middle points of the sides and have its center at the intersection of 
the diagonals. 

157. The major axis should always be drawn or imagined when drawing an ellipse and the curve should 
be made symmetrical on it. Having both axes given, mark the center of the ellipse and then spot points for 
the four ends of axes. Draw the curve through these four points. 

158. Referring to Fig. 33, B, let the plane of the circle partly shown by the arc HLK be parallel to the 
plane of projection. Let equal divisions be marked on it as indicated. Now revolve the circle on a line, CH, 
coincident with its diameter, until it projects as the ellipse of which one-half is SHJ. Any division point as L 
on the circle will, during the revolution, remain in a plane perpendicular to the axis and the projection of L 
will be found somewhere on a line LM perpendicular to CH. As the projection of L must also be on the ellipse, 
it will be found at M. ' 

It is seen, that equal divisions on the circle are not so on the ellipse, its projection, but that they shorten 
gradually toward the end of the major axis. This construction will give results of considerable accuracy, even 

50 




though drawn free-hand. When some knowledge of the rate of shortening is acquired, the construction may- 
be dispensed with. The gear teeth in the drawing were spaced by the eye and not quite accurately, as the con- 
struction shows. It is true, however, that the error is scarcely noticeable. 

159. Having a circle and one of its diameters, if a chord be drawn parallel to the diameter and bisected, 
a diameter through the point of bisection will be perpendicular to the first diameter. 
Now place the circle so its plane is obiique to the plane of projection and the pro- 
jection of the circle becomes an ellipse. The diameter and parallel chord project as 
parallels and the chord is still bisected. The projection is shown in Fig. 21. 

Having an ellipse ABCD representing a circle, and a line, 1-2, representing a 
diameter of that circle, to find the line representing a diameter perpendicular to 1-2, 
^'^- -^- construct as follows. Draw a chord 3-4 of the ellipse parallel to 1-2, bisect it at 5 

and draw the required line 6-1 through point 5 and 0, the center of the ellipse. 

160. The draftsman should acquire familiarity with the shape of various ellipses. Several should be 
constructed accurately by the method shown in Fig. 21. Draw two lines AB and CD at right angles and inter- 
secting at 0. On the straight edge of a strip of paper or card, mark FH equal to half the desired major axis 
and GH equal to half the desired minor axis. Place the paper so that F falls on the line COD and so G falls 
on the line AOB, then move the paper about, keeping F and G always on their respective lines. Mark point H 
on the drawing at its various positions and connect them. The curve will be an ellipse. 

161. Irregular figures are best drawn by plotting as shown in the line RS Fig. 34. Select a base line 
1-11 and divide it into equal parts. Erect a perpendicular or ordinate at each division point and measure off 
on it the required distance. 



Sr 



CHAPTER V 

SKETCHES FOR WORKING DRAWINGS 

162. If it is desired to have a sketch accurate as to shape and size, it should be made on cross section 

paper. The kind ruled in I" squares is preferable, though that ruled in J" squares is suitable for large drawings. 
If the piece has one or more axes of symmetry, these should be first drawn as center lines. If the piece 

has any prominent circular parts, the view showing them as circles should be drawn first. Thus, in Fig. 22, 

the lower view of the box cap is the one to be started first. The 
dimensions being given and the scale of the drawing being assumed 
as half size, draw a horizontal and a vertical center line through 
point A. Take the radius of the shaft and spot points B, C, D. 
Draw the semicircle BCD. Draw in succession BE, DF, GE, HF, 
JG, PK, LJ and MK. Spot points 0, N and P, and draw arc NOP. 
Draw LQ and MR then proceed to the top view. Draw center line 
Z-Z, then 1-2 and 3-4. By referring to the lower view, spot points 
5, 6, 7 and 8 and draw in order 1-7, 8-3, 2-5 and 6-4. By referring 
to the lower view, spot points 9, 10, 11 and 12 and draw in order 
9-10, 11-12, 9-13, 11-15, 10-14 and 12-16. Spot centers of bolt holes 
17 and 18 and draw circles. Spot 19 and 20 and draw arcs concen- 
tric with the bolt holes. Draw verticals at 5, 6, 7, and 8 to meet 
these arcs. Draw circle for oil hole. 

Return to front view and by projecting vertically from the top 

view, put in dotted lines for bolt and oil holes and the recesses cut for the nut. 

The order of drawing lines may be varied to some extent, but that given will enable the draftsman to 

do the work expeditiously and in ink without previous penciling. This is the kind of sketch which a designer 

most frequently uses in working out details. 











/ 


1 














1 


2 








































. 










'^ 







fH 














r- 7 






^ 










~ 




^^ 












~ 


f"" 


b- — 


















^- 


> 


\ 










/ 


f 


'^ 










z- 












■Lj 


— 


-(- 


-)- 


p 


4- 












■Z 








/7 




1 


iV 1 
















^^ 


J 


/ 










\ 


< 


*y 




















{ 














V. 
















\ 






^ 




















^ 


'. 




> 






s 


c 






^ 
















































5 














/ 



























^ 


-r 


-n 






















L 






0/ 


4 




1 


1 

1 




"N 


v; 






M 










/ 




■ 


f 




^ 


-^ 


rL- 


> 




V 






\ 
















1 , 


■ / 


/ 








\/ 


\ 














J 








t- 


7 










V 










K 








fs 


J 


f 


•3 
















' E 


B 






A 







F '^ 













Fig. 22. 



52 



RocKEfi Arm 

OaIE- MAL . /fiOf^-PAT. No. J9-?- 



COf?£ /-/OLES 



163. If the draftsman has to make a dimensioned sketch of a piece m place on the machine, a different 
procedure is advisable. The piece should be sketched, dimension lines and specifications added before any 
measurements are made. The purpose of this, is to avoid soiling and obliterating the drawing as much as possible. 
There is little advantage in making such a sketch on ruled paper, as the drawing is made by the eye. 

164. The piece to be sketched is the Rocker Arm shown in Fig. 23. It is covered with dirt and grease 
and cannot be removed from the machine. Before beginning the sketch, look the piece over carefully to deter- 
mine its character. 

Draw first the view showing the hubs as circles. Put in center lines X-X and Y-Y the angle between 
them being estimated by the eye. Spot centers of circles and 
draw all six beginning with the large hub. In estimating 
relative sizes, base the diameter of the large hub on the dis- 
tance between its center and the left hand center. Base the 
diameter of the small hubs on the diameter of the large one. 
Base the diameter of each hole on its own hub diameter. Next 
draw lines of arms basing the arm width on the small hub 
diameter. Proceed to the lower view, put in the center line 
Z-Z and vertical center lines for the holes. Mark on vertical 
center lines the lengths of hubs basing the measurement on 
the hub diameter. Draw ends of hubs, determining their side 
limits by reference to the upper view. In the same way, spot 
and draw the lines of the arms, basing their thickness on their 
width. Draw the vertical side lines of the , holes and hubs. 
The arms being filleted into the hubs, there will be no intersection line, but the shape of the joint may be 
suggested by a line, as shown in the drawing. By showing one-half the front view in section, the construction 
is seen at a glance, otherwise, dotted lines must be studied. Draw the outline of the arm section. Little draft 
is necessary on the hubs as they are short. 




■0^S^2^^ 



r-A 



w 



\ 






-/i-^ 



fT 



Fig. "23. 



53 



Next draw extension and dimension lines, but put on no figures. Make the measurements systematically, 
so none may be overlooked. The following order is satisfactory. Distance between centers of hubs; Angle 
of arms; Diameter and length of each hub and hole; AVidth and thickness of each arm. Put on dimension fig- 
ures distinctly and mark finished surfaces in the view where the surface projects as a line. Make the section 
lining last. Specify material, number required and the pattern number, if there be one. 

■ 165. If dimensions are known, and a sketch is to be made with some accuracy as to proportions, a scale 
can be improvised as shown in the drawing, if neither scale nor ruled paper are available. 

166. If sketches like the preceding are made in the systematic way indicated, they may be drawn directly 
in ink. The beginner should work witk ink from the start, as it trains him to look ahead and plan his drawing. 
He may spoil a few drawings at first, but a spoiled drawing is usually one of the most instructive lessons a drafts- 
man ever gets. 

CHECKING A WORKING DRAWING 

167. Even with the utmost care an error in a drawing will sometimes get by the inspector and appear 
in the finished machine or structure. Such errors may often be remedied, but sometimes they prove v(?ry costly. 
All reasonable precautions to avoid them should be taken. Not all drafting offices check their drawings, but 
most of them admit the desirability of doing so. 

No general brief rules can be laid down for checking a design as so many things have to be considered. 
A few things that easily creep in unnoticed are illustrated as follows. Interference of parts, as might happen 
with the feed handles on a lathe carriage : Holes that cannot possibly be drilled : Tee slots which the cutter 
cannot get into: Surfaces which a planer tool cannot reach: Castings with impossible coring. 

In checking a drawing, we shall examine to see if there are sufficient dimensions and specifications and 
if they are the right kind to secure correct construction. Important dimensions, such as center distances, will 
be scanned more carefully than others. Also we must compare corresponding dimensions of related parts to 
see if they agree. Thus the bearing on a spindle must agree with the bearing in the box. The diameter and 
pitch of a screw must agree with the same dimensions on the hole into which it goes. 

54 



The logical method is to take each piece by itself and putting yourself in the place of the workman go 
rapidly in imagination through each step in the process of making. Examine systematicall}^ the location, dimen- 
sions and specifications of each part of a piece. Where overall dimensions are given, see that thej^ agree with 
the sum^of the partial dimensions. Compare dimensions of fitted parts with the corresponding dimensions of" 
the related piece. See if finish marks are complete, also if material, number required and any special treatment 
is specified. 

To illustrate, take the Spur Gear in Fig. 13. Is it cast or cut from the solid bar? Are dimensions for 
the pattern maker complete? Look for outside diameter, thickness and diameter of cored hole. Is the finish 
fully specified? Are the dimensions for the machinist complete? He will first chuck and ream a 1" hole, then 
he will put the blank on an arbor, turn it to 21" diameter, and face up the sides to |" thick. The teeth will 
next be cut. How many? for setting the index. What number, kind and pitch of teeth? for selecting the cutter. 
The arbor is now knocked out and the keyway cut on the keyseater. What is its size? Where is the shaft on 
which this gear is to be keyed? Is the bearing for the gear 1" diameter and |" long and is there a J"Xj" key? 
These questions satisfactorily disposed of, the drawing may be considered checked. 

Many variations of this method of checking will be found desirable depending on the tj'pe of work con- 
sidered. It should be done always systematically to insure that every item is covered. If there are tapped 
holes, all might be considered at one time, examination being made for location, diameter, pitch and depth. 

CHAPTER VI 

GEOMETRIC PERSPECTIVE AND ARTISTS' PERSPECTIVE 

168. The method of making a Geometric Perspective drawing has been described in Chapter I. It 
was there pointed out, that such a drawing should be viewed from a particular point only, if it were to correctly 
represent the object. 

If one stands with his back against a wall, his arms outstretched on it and his eyes looking straight ahead, 
it is possible to detect motion of the hands. But though the angle of vision may be 180° or more, the angle 

55 



of distinct vision is certainly very small. In reading from a page held at the usual distance, the eye can see 
distinctly the word at which it is looking and indistinctly the word on either side. Beyond this, the ordinary 
eye does not see words distinctly enough to read them and has to be turned. 

If then, we are examining a long drawing, we do not stand close to it at its middle and turn the eyes 
or head so as to get an oblique view of its ends, but we move about and stand in front of each detail to be exam- 
ined. • It is for this reason, that geometric perspective drawings, so made that the eye embraces a large angle, 
are distortions offensive to the eye. Such a drawing would appear correct and without distortions if viewed 
from the right point, but it would be difficult to locate this point for an observer and it would be an unnatural 
and unsatisfactory way of looking at the drawing. 

Referring to Fig. 4, A, it is impossible for the human eye to see the front face of a cube as a perfect square 
and at the same time see the top and side faces. If the cube is placed so one face is seen as a perfect square, 
no other face is seen and if the cube be turned sufficiently to show a top and a side face also then the front face 
changes its shape, the top and bottom edges becoming inclined. 

Neither do we ever see a horizontal circle as a tilted ellipse, and the appearance of a sphere is always a 

circle. 

The photographic lens gives a true geometric perspective image and if on account of confined space, it 
is necessary to use what is called a "wide angle" lens, these distortions may become very great. We shall find 
in such photographs many curious representations, such as a sphere appearing as an oval solid similar to a hen's 
egg. - This is due, it should be remembered, not to any defect in the lens, but to the geometric perspective. The 
eye could see a sphere the same way, if the angle of distinct vision were great enough. 

169. Artists' Perspective shows an object as the eye sees it. Its results are similar to what would be 
obtained, if a spherical surface were used for the picture plane in a geometric perspective, the eye being placed 
at its center. As only a very small portion of such a surface may be considered approximately flat, the angle 
of vision is of small size. A panoramic photograph is a near approach to an artists' perspective, but inspection 
of one of these, shows new misrepresentations. The perspective is violated seriously in the matter of converg- 
ence of lines. 

56 



It is therefore the province of the artists' perspective to harmonize all these incongruities and produce 
a drawing which, though not scientifically correct, produces a pleasing and satisfactory effect on the eye. 

170. We have seen in Chapter I, that a projection drawing is simply a perspective made with the eye 
at a great distance from the object. 

We have also noted the following facts about projection, namely, 

Lines oblique to the plane of projection do not project in their true lengths, but are foreshortened. 
The angle between two lines does not project in its true size, except under certain peculiar conditions. 
The projections of parallel lines are parallel. 

Equal divisions on a straight line will project as equal divisions. 
Lines parallel to the plane of projection project in their true size and shape. 
Equal and parallel figures project in equal and parallel figures, though not the same as the original. 
It remains, to discover how these results will be changed, when the eye is brought close to 
the object. 

171. The following principles are based on observation, but they may be proved by geometry. The 
line of sight is the line along which the eye looks at the object, just as in aiming a 
gun. The picture plane is always perpendicular to the line of sight. of pyi/f^iL£/.s 

172. In Fig. 24, is shown a ladder lying on the ground. Observe that lines 
which are parallel in the object, converge in the drawing. Fig. 31. shows the effect 
of non-convergence. 

173. Comparing the convergence of the rungs with the convergence of the ^/ eouJ^spaces'' 
sides of the ladder, observe that the nearer lines are to being parallel with the line of 
sight, the greater their convergence. 




Fig. 24. 



174. Parallels which are perpendicular to the line of sight show no convergence and if equal in length, 
the one furthest from the eye appears shortest. 

.S7 



V.P30°LEFT V.P4-S°L. 



EYE M 



if.R4-5R. 



V.P30°ftl6HT 



175. Exception. Though vertical parallels may appear to converge, they never are drawn so. See 
Section G, and Fig. 3. 

176. In Fig. 25 is a Geometric Perspective drawing of a regular hexagon resting flat on a horizontal 
plane. Two opposite sides and their parallel diagonal constitute a series of parallel lines. There are thus three 
series, each having its own direction. Note that the lines of each series converge toward the same point. This 
point is called the vanishing point of the series, because if the lines were unlimited in length, they would dis- 
appear at that point in the drawing. This may be seen on a long, straight stretch of railroad track. 

177. Note in Fig. 25 that the three vanishing points 
for the sides and diagonals are on the same horizontal 
line. 

All series of parallel lines which are parallel to the 
horizontal plane will have their vanishing points on the 
same horizontal line. This is called the Horizon Line. 

178. Notice in Fig. 24, that though the rungs of 
the ladder are equally spaced, those furthest away appear 
closest .together. 

If a straight line is divided into equal parts, those 
parts furthest from the eye appear shortest and the length gradually increases as 
they get nearer the eye. 

This may be seen in the spacing of ties on the railroad and on a picket fence. 

179. Fig. 26 is a drawing of three equal pulleys on a shaft. Note the 
difference in the shapes of the ellipses. 

In a series of circles, the one whose plane is parallel to the line of sight appears 
as a straight line, the one whose plane is perpendicular to the line of sight appears as a 
true circle, while circles having intermediate positions appear as ellipses with 
varying degrees of narrowness. This principle applies to other figures as well as to circles. 

58 




P£ffP£^a/Ciy^A^ TO 7-H£ 
PfCTUf?£ F'l.'QNE. 

L INEAR^ F£RSPECT/ye 
'Scale e j/^ch = I foor 



EYE. (H) 

Fig. 25. 



■5/0£S CO/vy£/=7if£^ TO A 

Po/nr o/v THa Hof^iZ-ON 




F£RS/>£CriV£ 

OF Pa/^ALLLL CtfiCLES 

Fig. 26. 



It may be seen illustrated in long cylindrical forms such as boilers, tanks and pipes. 

i8o. With the exception of the variations stated in Sections 172 to 179 inclusive, the principles of pro- 
jection drawings apply equally well to perspective drawings. 

MODEL DRAWING 

i8i. A course in model drawing from the object is of value for several reasons. It gives familiarity 
with the peculiarities of artificial type forms that are found singly or combined in all engineering constructions. 
It trains the faculty of observation. A drawing of a squash may be satisfactory, yet not much like the original. 
A drawing of a prism, a pyramid, a cylinder, a ring, a cone must be very nearly correct or the error is apparent 
to all. Third, it gives dexterity in handling the pencil or pen. 

182. The following models taken in order will give a progressive set of exercises sufficienth' comprehensive. 
Place them on the table or floor below the eye level and draw them in various positions. While doing this verify 
and apply the principles of projection and perspective which have been previously stated in Sections 170 to 179 
inclusive. A — Cube, B — Scjuare Prism on end, and on side, C — Square Frame lying flat and upright, D — 
Triangular Prism on end and on side, E — Triangular Frame lying flat and upright, F — Hexagonal Prism on 
end and on side,G — Hexagonal Frame lying flat and upright, H — Square Pyramid on base antl on side, I — 
Hexagonal Pyramid on base and on side, J — Cylinder on end and on side, K — Half Cylinder on end and on 
flat side, L — Flat Ring lying flat and upright, M — Cone on base and on side, N — Sphere, — Hemisphere lying 
on flat surface and on curved surface, P — Torus Ring lying flat and upright. 

183. When making a perspective sketch of an object, hold the drawing board in an upright position 
so its plane is perpendicular to your sight as you look down on it. It should be held low enough, so you can 
look over its upper edge at the object and then back again at the drawing with only a slight mo^Tment of the 
head. 

Before beginning to draw, read again Sections 170 to 179 inclusive and the suggestions in Chapter lY 
and endeavor to apply them. Refer to them continually if you wish to be successful. 

59 



Make your drawings of generous proportions. It may be easier to draw a short line than a long one, 
but it is more difficult to get proportions correct in a small drawing than in a large one. 

184. Suppose it is desired to make a sketch of the cube as shown in Fig. 27. 

Sit back in your chair in an erect position with the drawing board resting in an upright slanting position 

on the knees. When looking at or testing the lines of the object, be careful to occupy always the same position. 

■ Proceed in the following order. Draw verticals of indefi'nite length to represent the vertical edges of 

the right face. Estimating with the eye, decide on the relative horizontal widths of the vertical faces, then draw 

the left vertical of the left face. Take a point B on the middle vertical and 
judging the inclination by the eye, draw the top edge of the left face. In the 
same way, draw the top edge of the right face. The inclination of these 
lines may be more accurately judged, if the eyes are closed until the lines 
are just visible. The draftsman may hastily conclude that the back edges of 
the top face appear parallel to the corresponding front edges, but careful 
scrutiny with partly closed eyes will prove the contrary to be true. Having 
decided on their inclination, draw them, completing the top face. Next, 
estimate the length of the middle vertical, comparing with the horizontal 
width of the right face. Mark its length and draw the bottom edges of the 
side faces in the same way as the top edges. 
The drawing should look pretty "scratchy" by this time if the instructions in Section 138 have been 
followed. 

185. Now test the drawing by comparing lengths of lines and other suitable dimensions, and by 
measuring inclinations of lines. 

Remember that it is the apparent lengths and not the true lengths of lines of the object which are to be 
compared. 

To compare lengths of the front edges of the top face, sit in the same position as when drawing them. 
Grasp the pencil at one end by the fingers of the right hand, leaving the thumb free to be moved back and forth 

60 




Fig. 27. 



on the projecting part of the pencil. Without moving the body, stretch out the arm straight to full length, 
then swinging the arm from the shoulder, bring the pencil so it appears near the right front edge of the top face. 
Now turn the hand, or the pencil in the hand until the pencil is perpendicular to the line of sight. Swing the 
arm slightly and rotate the arm in the sleeve until the pencil appears to coincide with the line, the end of the 
pencil being at one end B, of the line. Move the point of the thumb along the pencil until it coincides with the 
right end of the line. The length on the pencil from its point to. the thumb is the apparent length of the line. 
Without removing the thumb, swing and rotate the arm so as to bring the pencil to lie along the line AB with 
its end on A. Be sure the pencil is perpendicular to the line of sight. Note now, how the point B appears to 
divide the length from the end of the pencil to the thumb. Is it one-half, three-eighths or what? Having decided, 
compare the lengths of the same lines in the drawing. 

In making these measurements the pencil must always be held at arm's length and perpendicular to the 
line of sight or the results of the test will be worthless. 

i86. To test the inclination of any line as AB, sit in the same position as when drawing the line. Place 
the board so its upper edge is horizontal and incline it until its plane is perpendicular to the line of sight. Take 
the pencil or a straight edge and lay it flat against the face of the board allowing several inches to extend beyond 
the edge as shown in Fig. 27. Look straight at the line AB to be tested and without moving the head, move 
the straight edge about on the surface of the board till it appears to coincide with AB. Holding it in this position, 
look immediately at the corresponding line in the drawing and note if it is parallel to the straight edge. After 
some practice in this way, it will be found accurate enough and quicker to judge of the inclination of the line 
by half closing the eyes and comparing with a pencil held horizontal. Then quickly place the pencil horizontally 
on the drawing next the line being tested and note if the angle is the same. 

Test the drawing until the correct lengths and inclinations are established, then remove superfluous lines. 
By using light sketch lines, this task will not be an arduous one. 

187. When drawing cylindrical forms, draw the ellipse first after establishing the slant of the major axis 
and the ratio of lengths of axes. Then draw the straight side lines, being careful that their direction is such 
as to make the axis of the cylinder perpendicular to the major axis of the ellipse. 

6t 



CHAPTER VII 



AXOMETRIC SKETCHING 

i88. At Fig. 28, A, is shown the projection on a vertical plane of a square parallel to it. Take an axis 
line X-X in the plane of the square and through its center. If the square be revolved 
on this axis until its plane is perpendicular to the plane of projection, its projection 
will be a straight line as shown at E. 

Intermediate positions will give projections as at B, C and D. 

In the original projection at A, draw the horizontal QR, the verticals -MQ and 
OR. The triangles MPQ and OPR are equal and the following proportion is true. 

MQ PR 

= . When the square is revolved, these triangles change their form 

OR PQ 

in the projection, but it can be proved that the proportion is true for all positions 

between the extremes mentioned. 

1 

189. This fact gives at once a quick way for drawing the projection of a 
square which is oblique to the plane of projection. Referring to Fig. 28, C. let it be 
required to construct the projection of a square so placed that the ratio of horizontal 
distances between its three nearer corners is |-. That is PR = 3PQ. 

Draw QR any desired length and take point P so PR = 3PQ. Erect verticals 
W at Q and R. Draw MP at any desired inclination not greater than MP in A. Make 
I OR the same fractional part of MQ that PQ, is of PR, in this case ^. Draw OP and 




OR the same fractional part of MQ that PQ is of PR, in this case 
MN parallel to it. Draw NO parallel to MP. 



Fig. 



190. If the true length of side of the square represented is desired, it can be found 
by noting from Fig. 28, A, that it is the hypothenuse in a right triangle whose legs are equal to PQ and PR. 

62 



iQi- In Fig. 29, the projection CDEF of a square has been drawn by the method of Section 189. AC = 
2BC and BD = 2AE. To complete the cube of which this sciuare is the top face drop verticals at C, D and E. 
Draw trial lines for the bottom edges GH and HJ, placing them so as to make the figure look like a cube. Now 
turn the drawing around until CDHJ becomes the top face and note if the drawing is still a good representation 
of the cube. It will probably be too tall or too short. Change the lines GH and HJ until the drawing looks 
like a cube in either position. 

The exact length of the verticals can be found by construction, but the method described is sufficiently 
accurate and much quicker. 

192. Find the center K, of the top face by the intersection of diagonals and draw PT through it per- 
pendicular to CH. Mark the middle points of the sides of the top face 
and sketch in the ellipse which isfhe projection of the inscribed circle. Draw 
the ellipses for the other two faces, being careful to get the correct slant 
for the major axis. When completed, the three major axes should measure the 
same, if the work is accurate. 

Divide CE, CD, CH and PT into eight equal parts each. 

193. The three lines CE, CD and CH represent lines actually perpen- 
dicular and of equal length. They may be considered as axis lines of length, 
breadth and thickness. If the cube which this projection represents were a 
1" cube, then the projection of any other rectangular solid could be easily 
drawn by imagining the object placed with its edges parallel to those 0'' the 
cube. Direct comparison could then be made between the lines in the 
projections of the two objects. 

A circle in any face of the rectangular solid would be represented by an ellipse of the same shape as that 
in"' the parallel face of the cube. The size of the ellipse would be determined by a comparison of its major 
axis directly with that of the ellipse in the cube. 

63 




Fig. 29. 



AXOMETRIC ShETCH 



TO Hey Cube.. 



194. In Fig. 30 is a sketch made in the manner just outUned. The object is the Hoist Arm Yoke whose 
dimensions are given in Fig. 10. The drawing is made of small size by assuming that the reference cube used, 
that of Fig. 29, is 4" on an edge. 

At a point draw three axis lines OX, OY and OZ parallel respectively to lines CD, CE and CH of the 
reference cube. For convenience in measurement, lay off from on OX a length equal to \ of CD, a length equal 

to \ of CE on OY and on OZ a length equal to \ of CH. Each 
of these lengths represents an inch measured in the direction 
of its axis. These lengths are divided into quarters. 

'^ Following the dimensions as given in Fig. 10 make OA 

7", OB 2|" and OC 2". Draw CD parallel to OA, AE and CG 
parallel to OB, AD and BG parallel to OC. Make AE equal 
to OB then draw EH and FB parallel to OA and f " long. Draw 
HR and FS parallel to OB and 2i" long. Draw RS parallel to 
OA. Mark point J so that CJ equals 3i". Make JK f", KN 
li", and KQ If. Draw in order QP, "JL, PN, PM, NL and 
ML, parallels to the lines of the ear first drawn. Make OU \" 
and draw a parallel to OB through U. Make CT 2\" and draw 
a vertical through T. The intersection of these two lines is 
the center of the f" tapped hole. Draw the major axis of the ellipse perpendicular to OA and base its length 
on the line PT of the reference cube of Fig. 29. Draw the ellipse the same shape as that in the right face 
of the reference cube. The hole in the ear is located and the ellipse drawn in a similar manner. The 
shape of this ellipse will be like that in the top face of the reference cube and its major axis is perpendicular 
toOC. 

The projection of any object, however complicated, may be drawn in this way, if its dimensions are known. 
As an endless variety of reference cubes can be constructed, it is always possible to select the most suitable 
position for representing the object. 

64 




Hour Arm yoHE 



Fig. 30. 




AxOM£T/9ir 
MoOZ/^/CO B Y 
COf^i/SKGCNCC: 
Of PAfiALLCLS 




Fig. 31. 



195. A drawing made in this way is called an Axometric Drawing, because the directions and measurements 
of lines are referred to axes representing the three principal dimensions of an object; length, breadth and thickness. 

196. If Fig. 30 is held at arm's length it looks correct, but from 
the usual distance of about 12" the further ellges appear longer than the 
near ones and the lines supposed to be parallel appear to diverge away 
from the eye. Correct the drawing by shortening the lines until they look 
right and converge the parallels until they look parallel. In other words, 
modify the drawing, so it will not violate the principles of perspective. 
In Fig. 31 is an axometric drawing of a center rest jaw. Note that the 
back corner appears tilted up and the back end appears larger than the 
front end. The second drawing shows the axometric drawing modified 
by introducing convergence of parallels. Although changes in the 
drawing are slight, the change in appearance is marked. 

197. In Fig. 32, are shown a number of drawings of type forms made in the way just described. At R, is a 
box cap composed of a semi-circular shell with two ears. The complete elliptical end should be sketched in as indi- 
cated by the dotted lines, until the draftsman has become familiar with the appearance of the half cylinder form. 

198. In the case of truncated pyramid or cone forms, work with the vertex as shown in D and T. 

199. Where two irregular curves are placed symmetrically, draw the axis of symmetry first and plot 
the curves either side as in U. 

200. The nut at K was constructed by first drawing the complete base, then all the faces, last the ellip- 
ses and the contour at the right of them. To get the curve at the top of a face, plot its middle and end points. 
This is an Isometric drawing. 

20T. At H is a drawing of the Spiral Gear Shaft of Fig. 10. Draw center line first and mark centers 
of ellipses dividing into proper lengths by the eye. Draw ellipses, observing the perspective effect of distance, 
then draw the straight sides with convergence. 

65 



202. Threads are drawn somewhat conventionally. A series of parallel ellipses with their major axes 
not quite perpendicular to the axis of the screw will be fairly suggestive of a screw thread. The shape of the 
ellipse should be the same as the end of the cylinder on which the thread is cut. Look out for spaces and the 
shape of the curve at the side line where it forms a slight notch. Threads are shown at D, E, G and H. 

203. At F is a rapid sketch of a coil spring. If done accurately, the point of the loop on the right would 
be horizontally opposite the space between points on the left. 

204. At G is half of a Flange Union such as S of Fig. 14. Draw the central ellipse first, then the four 
small ellipses representing bosses for the bolts. The centers of the four are on lines at right angles in the object. 
Apply method of Section 159 to determine these lines. 

After completing the upper ellipses, drop verticals and draw parallels to the upper curves. This is an 
axometric drawing without perspective modification. Note how the left side appears tilted, because of this. 
All of these ellipses have horizontal major axes. 

205. In the washer at N, sketch bottom ellipse complete before drawing side curves. 

206. At E is a straight coupling like A of Fig. 14. Note how the effect of a rounded edge on the end 
is produced. 

207. The character of a surface is often brought out by the curvature of lines on it. This is particularly 
true, of spherical surfaces. Note this in the Binder Handle at S, Fig. 32. Observe that the major axis of the 
ellipse representing the flat place on the ball is perpendicular to a radius of the sphere drawn from its center. 

Straight lines for the slot on B would convert the curved top into a flat one. 

At C note that the outline of the hemisphere is made up of a serai-circle and a semi-ellipse. Also notice 
how the curved lines of the slot are determined. 

208. At Q, Fig. 32, is shown a torus ring, a form occurring in valve handles, hand wheels, pipe returns 
and bends. 

If we take equal paper circles, each with a small hole at its center, and fill a wire circular hoop with 
them, we shall have a torus ring. Each circle will adjust itself so its plane is perpendicular to the wire at the 

66 




Fig. 32. 



point where it is situated. A projection of the wire hoop would be an elUpse, as shown in the dotted hne in 
Q. Each paper circle would project as an ellipse. The major axis of each ellipse would be perpendicular to the 
curve of the wire i.e. to the curve of the large ellipse. Major axes of all the small ellipses would be equal. If 
all the small ellipses were drawn and a tangent contour to them made, we should get the outline of the ring. 
This outline is thus composed of curves parallel to the elliptical center line. One extreme position will show 
the ring as two concentric circles. The other extreme, shows it as two semi-circles connected by parallel lines. 

209. If it is desired to draw a return bend like J of Fig. 14, draw the complete torus ring and cut 
it in halves as shown by dotted lines in Q, Fig. 32. To draw the small ellipse which represents the circular cut, 
draw the major axis perpendicular to \he large ellipse curve at that point. A second diameter of the small 
ellipse, (not the minor axis) is found on the end of the oblique diameter of the large ellipse. From the relation 
of the lines the following proportion is true. 

Oblique diameter of small ellipse , Major axis of small ellipse 

Oblique diameter of large ellipse Major axis of large ellipse. 

If a quarter turn is desired, the ring may be divided into quarters in the same way and by use of the 
construction of Section 159. 

210. At L and M are shown chain and rope as they appear when hanging vertical. 

211. In sketches of sheet metal work, it is often desired to show the intersection of various surfaces. 
A pure guess will generally result in a bad representation, unless the draftsman is familiar with the different 
intersection curves. 

If the draftsman understands the construction of intersection curves by means of parallel cutting planes, 
the following method will prove useful. 

In A, Fig. 32, is given a vertical cylinder whose axis is along 1-2. It is intersected by a cylinder whose 
axis 2-3 is perpendicular to that of the large cylinder at its middle point 2. The diameter of the small cylinder 
is one-half that of the large and its axis 2-3 is equal to the diameter of the large cylinder. 

68 



Having drawn the projection of the large cylinder as desired, find the middle point, 2, of its axis. Draw 
the axis 2-3 of the small cylinder at any desired inclination. To find 3, draw 4-5 parallel to 2-3 and make 2-3 
equal to 4-5. Draw the major axis of the ellipse perpendicular to 2-3 and make its length half that of the 
of the ellipse of the large cylinder. To find a second diameter of the ellipse (not its minor axis), draw 8-9 a 
diameter perpendicular to 4-5 by the method of Section 159. Draw C-D parallel to 8-9 and of length equal to 8-1. 

In the actual object 8-9 is perpendicular to 4-5 and to 1-2, therefore perpendicular to the plane 1-2-3 E 
of the axes of the cylinders. The line C-D being parallel to 8-9 is perpendicular to the same plane, therefore 
perpendicular to the line 2-3. Line C-D must then be in the plane of the end of the small cylinder. 

Draw the ellipse through points C, D and the extremities of the major axis, making it symmetrical on 
the latter. 

212. To find the intersection, draw first the line FEG which is the intersection of the planes of the ends 
of the cylinders. Cut both cylinders with a plane HJKL which is parallel to the plane of their axes. This plane 
will cut an element out of each cylinder, thus LH from the small and LK out of the large cylinder. These two 
lines intersect at point L which must therefore be a point common to both surfaces, or a point in their inter- 
section. Other points may be found in the same way. Three or four are usually sufficient including those for 
the side lines of the small cylinder. 

213. It may be objected, that the errors in making such a construction free-hand will give worthless 
results. Experience of many years use with beginners has proved the contrary. The method with all its errors 
will give results far superior to those of a guess and with a trifling expenditure of time. 

214. The Axometric Drawing gives us a rapid and accurate method for making a free-hand perspective 
drawing of an artificial object without the object or any drawing thereof, provided its construction and dimen- 
sions are known. 

The method briefly stated is this. First, construct a reference cube. Second, by comparison with it 
make an Axometric Drawing of the object. Third, change this Axometric Drawing into a Perspective Drawing 
by applying the common perspective principles. 
69 



After the draftsman has followed this method for a time, he finds he can dispense with the reference cube 
and that he can introduce the perspective as he draws his lines. In other words, he has learned to make a per- 
spective sketch of an object not before him and can therefore reproduce in this way what exists only in his mind. 
Such ability is of the highest value to the designer. 

215. In Fig. 33 are rapid sketches of gearing which give a test of the application of the method. The 
least possible construction was employed in each case and most of this is shown in dotted lines. Auxiliary sketches 
indicate the way in which the drawings were built. 



CHAPTER VIII 

ISOMETRIC DRAWINGS AND CABINET 




Fig. 34. 



PROJECTIONS 

216. In Fig. 6, C, is shown the pro- 
jection of a cube obtained by placing the 
cube so its dimensions of length, breadth 
and thickness make equal angles with the 
plane of projection. It does not other- 
wise diiTer from any ordinary projection. 
It is called an Isometric Projection. In 
Fig. 34 is shown such a projection of a Ij" 
Cube. The edges in the projection will be 
less than 1|" because of fore-shortening. 
In the same figure, is a drawing similar to 
the projection, but larger. In this draw- 
ing, the lines representing the edges of the 
cube are just Ij" long. This is called an 
Isometric Drawing. It is a special form 
of an Axometric Drawing, and all the 

7o 



Sketches from Workinq Drawings 




Fig. 33. 



principles and methods applicable to the latter apply to it. Its peculiarities are as follows. The axes of 
reference, BA, BG and BC are 120° apart, and a unit length on any one of them will measure the same as on 
any other. Thus the edges of the cube will all be of the same length in such a drawing. One scale for 
measurement is therefore needed, instead of three as in axometric. The line BC is usually vertical and this 

makes AB and BG 30° lines. Ellipses for all three planes are also the same 

shape and similarly placed relative to the axis of reference. The major axis 

of the ellipse for each side face is inclined 60°. 

It is obvious that an Isometric Drawing is the simplest kind of an 

Axometric Drawing and that it is particularly adapted for instrumental 

construction. 

217. Referring to the Isometric Drawing of Fig. 34, two methods 
are shown for drawing the Isometric Ellipse. The one in the top face of 
the cube is an exact construction for the eight points used. These points 
are the middle points of the sides and the extremities of the major and 
minor axes. Point P is found from point L by the construction indicated. 
LO is parallel to AB. 

In the right face is shown a method employing circular arcs with cen- 
ters at H, B, J and K. The method is approximate only, the error being 
indicated by the dotted arc with G as a center. 

The approximate ellipse should never be used as an intermediate 
construction for getting other figures. In the left face is shown a method 
for drawing irregular figures of any kind by plotting. 

218. In Fig. 32, K, is shown an isometric drawing of a hexagonal 
nut. See also, Section 149 for its construction. 

219. Isometric cross section paper is obtainable and affords a very 
convenient way for making an isometric sketch. Such an one is shown in 

72 






Fig. 35. 



Fig. 35 with complete dimensions. No explanation is necessary, beyond saying that ellipses should be drawn 
before the side lines of the cylinders. Such a drawing can be easily scaled. It is half size. 

CABINET PROJECTIONS 

220. In Chapter I, it was explained that Cabinet Projection is a special kind of Oblique Projection 
obtained by placing the object and taking the projecting lines in a peculiar way. The typical form of this pro- 
jection is shown in Fig. 4, B. 

The customary way to make the drawing is to draw one face in its true size and shape. Lines perpen- 
dicular to this face are drawn at 45° and one-half their true length. 

A circle in the front face is therefore drawn as a circle, but in a side face it would be drawn as an ellipse. 
The method for the ellipse in the side face is shown in Fig. 4, A. The 
curve is drawn through the middle points of the sides of the circum- p^J^^r/oN 
scribed square. Four other points are found on the diagonals from 
points a and b in the front face. 






221. 

dimensions. 



Fig. 36 shows a Cabinet Projection with complete 



222. Oblique projections, similar to cabinet projections, are 
often used in which the front face is shown in its true size and shape 
while edges perpendicular to this face are drawn at any convenient 
angle and made any convenient length not over full size. Fig. 7 is 
such a drawing. Edges perpendicular to the front face are 30° lines 
and their lengths are one-quarter size. 




Fig. 36. 



73 



CHAPTER IX 

COMPARISON OF METHODS OF REPRESENTATION 

223. The different methods of representation are not equally adapted to all purposes. The following 
comparison may not be agreed on by all draftsmen, but it is a fair statement. Isometric Projection is not con- 
sidered, as it is not used. An Isometric Drawing has all its advantages without its difficulty of scaling. 

GEOMETRIC PERSPECTIVE 

224. Pictorially, a drawing ot this kind may be very satisfactory if the visual angle is small. It has 
several unavoidable and objectionable distortions such as the tilting of the horizontal ellipse. It is not well 
adapted for rapid execution on account of necessary construction. Such a drawing should be made with instru- 
ments to secure a proper amount of accuracy. It is not adapted to dimensioning because of convergence of 
parallels. It cannot be used as a working drawing, because it cannot be scaled and because of the confusion 
caused by hidden lines and full lines of the object. Though its underlying principles are comparatively simple 
they are not quickly grasped. 

A drawing of this kind is especially useful for architectural drawings of buildings and manufacturing 
plants, and is sometimes the only way in which they can be represented. A photograph is a true perspective 
and less expensive, but in many confined situations, a photograph cannot be made. Fig. 2, A, is a Geometric 
Perspective Drawing. 

ARTISTS' PERSPECTIVE BASED ON AXOMETRIC 

225. Pictorially, this is the most satisfactory of all drawings. It has no distortions and is therefore 
pleasing to the eye. It can be made free-hand with great rapidity, but not so rapidly with instruments. It is 
not adapted for dimensions, nor for working drawings, because of the convergence of parallels and because every- 
thing is crowded into one view. The principles on which it is based are simple and its methods are quickly 
acquired. 

74 



It is undoubtedly the best kind o!" a sketch for rapid and forcible free-hand illustration of the details of 
engineering construction. 

COMMON PROJECTIONS 

226. Pictorially, a drawing of this kind is apt to be deficient, because some study may be required in 
reading it. This will depend on the simplicity of the object. Hidden lines can be represented with less confusion 
than in any other kind of drawing. It has no distortions. It is adapted to rapid execution free-hand and still 
better adapted to instrumental drawing because of its verticals, horizontals and circles which predominate. 
On account of the possible multiplication of views its carrying capacity for dimensions and specifications exceeds 
that of any other drawing. Neither can the meaning of a dimension be misunderstood. Its principles are 
simple and quickly learned. 

It is above all the best drawing for use in construction. 

ISOMETRIC DRAWINGS 

227. Pictorially, this kind of a drawing lacks the distortions of a Geometric Perspective and possesses 
those due to lack of convergence. The available positions of the object are very limited. Overlapping of parts 
and coincidence of lines often makes it difficult to read. It is adapted to rapid execution especially with instru- 
ments and of all the drawings showing three dimensions, it is the best adapted for dimensioning. It is often 
used as a working drawing for simple parts. It is simple in theory, usually easily understood and applied. A 
drawing of this kind is used considerably for showing interiors of buildings and details of construction, as it can 
be quickly drawn with instruments. Fig. 6, A, is an Isometric drawing. It is better adapted for this illustra- 
tion than a Geometric Perspective, because convergence of the projection lines would give a wrong impression 
to a student. 

OBLIQUE PROJECTIONS 

228. A drawing of this kind possesses all the objectionable distortions of Geometric Perspective. Many 
draftsttien approve of it, because of its resemblance to Geometric Perspective, forgetting that its resemblance 

75. 



is only of the worst features. More than this, it has the distortions of Axometric and Isometric, namely, lack 
of convergence of parallels.. Its principle virtue is that it can be quickly made free-hand or with instruments. 
It is not suitable for a working drawing as Fig. 36 will suggest. It should never be used for representing curved 
forms on account of the violent distortions. 

In spite of its deficiencies, it is often useful. Fig. 7 is an Oblique Projection and it is better adapted to 
the conditions than a Perspective or Axometric would have been. A Perspective would not have permitted 
parallel projection lines, but would have permitted bringing all faces of the cube to a position showing their 
true shape. An Axometric would have satisfied the first condition, but not the second. A Cabinet Projection 
would have met both conditions satisfactorily, but would have caused bad overlapping of views. 

CABINET PROJECTIONS 

229. Cabinet Projections have all the deficiencies that can be imagined. They have the bad distortions 
of Geometric Perspective, the distortions of Axometric the limitations of position which Isometric has. Never 
use it for anything, but rectangular forms. Fig. 36 shows how poorly it is adapted for a working drawing. . 

CHAPTER X 

FREE-HAND LETTERING. 

230. Although many styles of alphabets have been devised, only a few of them are adapted to rapid 
off-hand work or otherwise suitable for drawings used in construction. The novice is often confused in his'selec- 
tion by the great wealth of available material, and it is partly for the purpose of avoiding this that a veiy lim- 
ited number of styles has been presented here. If one masters thoroughly the single stroke Gothic, he will have 
little difficulty with any other style. 

Any free-hand lettering looks well, if it conforms to certain fundamental principles which insure uni- 
formity in general appearance. For this reason the plainest letters, if well made, are often quite as effective 
as more ornate ones. While the general tendency is toward the use of the simpler forms, the decorative styles 

76 



are also in frequent demand by the draftsman. These could not be satisfactorily included in such a brief treatment 
of the subject, but the treatises by Brown, Day and Strange provide all that could be desired along this line. 
A comparison of the contents of these books with the collections of alphabets formerly published for the use 
of draftsmen will afford considerable instruction in lettering as a fine art. To inlay the surface of a letter 
with mosaics and geometric designs or to drape it with biological rarities, does not make it beautiful. As a 
thing for use, its form should be recognizable, but beside this it may have so graceful a shape that there is 
pleasure in looking at it. 

Good lettering on a poor drawing will not redeem the drawing, but a good drawing may have its appear- 
ance ruined by poor lettering. Poor lettering affects our estimate of a draftsman's ability in about the same way 
that illegible handwriting impresses us regarding the writer. Ability to letter well depends on the same qual- 
ities as free-hand drawing. It is needless therefore for a student to say he cannot letter well, that he has no 
talent, is no artist. For what he calls talent is merely the natural ability to observe correctly, combined with 
muscular control. Inasmuch as both these powers may be acquired without excessive exertion, he can learn free- 
hand lettering by a little expenditure of reason and will. 

231. Mechanical lettering differs from free-hand lettering in that the letters in their final forms are 
made with instruments although they may have been first sketched free-hand. The curved parts are lined first 
by means of the compass or curved ruler, straight parts with the tee square and triangles. A combination of 
mechanical straight parts and free-hand curved parts is usually unsatisfactory unless the draftsman is an expert. 
Care regarding tangencies of straight lines and curves is as essential as in geometric drawing, so the process is 
apt to be a tedious one. This excessive amount of time devoted to a minor matter constitutes the chief objec- 
tion to the use of mechanical lettering on commercial drawings. From an artistic standpoint, a mechanical 
letter is often objectionable on account of its extreme precision and exact duplication, just as a piece of machine 
carving is less pleasing than that done by hand. With free-hand letters, this lack of flexibility does not exist 
because slight variations are unavoidable and no two As or Bs or Cs will be exactly alike. 

232. While mechanical or free-hand letters may be well formed and satisfactory as letters yet they may 
not harmonize with their surroundings. Imagine the appearance of Old English type on a working drawing, 

77 



or, if you will, the plain modern Gothic entwined with the traceries of a Moorish archway. The primary object 
of words is to say something. If the statement be in the form of a notice, the simpler the expression and the 
plainer the letters the better. If however we have a scriptural quotation used to fill bare space on a church 
wall, then something ornamental is desirable. Thus the question of lettering quickly merges into one of deco- 
rative design and the simpler forms of letters will be found modified into unusual shapes more or less artistic 
as will be seen by reference to memorial tablets, book covers and magazine advertisements. 

233. Students (generally poor letterers ) will often say, "Why should a draftsman learn to letter well; 
don't most drafting offices employ a boy to do such work?" Their idea is, of course, that in the development 
of the division of labor in the drafting office, the first man makes a sketch of the design of a machine, a second 
man elaborates details in pencil, a third makes a tracing of these in ink, a fourth puts on dimensions and a fifth 
the lettering. This may be all right in theory and it is in part the practice in some large establishments. In 
the great majority of cases, however, it will be found that the draftsman who begins the drawing does all the 
work on it. The only printing he may sometimes avoid is that for the title. In this matter practice varies, 
but the end in view is to secure uniformity and to economise time. It is for this reason that a boy who has 
a natural knack for lettering is often employed at low wages to put in all general and sometimes the sub-titles. 
The general title is often printed on a press with blank spaces to be filled in ; or it is printed with rubber type 
and lined over to make the letters opaque for blue printing; or the title is traced from a copy placed underneath. 
The dimension figures and printed specifications are put on by the draftsman who knows the drawing. And 
these dimensicn figures especially must be so definite in form and prominent in size that they are not easily 
obliterated even in the blue print. Too much care cannot be exercised in this particular for a slight irregularity 
in the drawing may cost hundreds of dollars to rectify when it has been duplicated in hard metal. A beam too 
short or a bearing out of place is an error not easily corrected and the responsible draftsman will pass through 
an uncomfortable season. 

FUNDAMENTAL PRINCIPLES 

234. Height and Width cf Letters. The underlying characteristic of good lettering is uniformity in 
general appearance. This applies first to the height and width or to the apparent area covered by the individual 

78 



' ,MUjnuhi[]HniKiuMN(m i 




2 £, 

J 



MBODjEF&HlUHiL MNOPQR 



4 
5 



t^iHiJM\A^iXJM:/UH,'mNni.^^ m 



SVUVWX YZ 'I2S4SB 7890 




^ AECDEFEHIJKLMNDPPRSTU 
10 VWXYZE. Fob Titles I234SE7B3n 



Fig. 37. 



letter. Referring to Fig. 37, lines 1 and 4, we see that all the capital letters are of the same height and nearly- 
all have the same width which we may stjde the normal width. The exceptions are the I, the J which is roughly 
I, the M which is ^ and the W which it| of the normal width. Figures are about | of normal width. Looking 
at the small or lower case letters of this alphabet we see in line 7 that the heights are variable. There is, first 
of all, a body in nearly all the letters, of a height equal to | that of the capitals. Six of the letters, b d f h k 1, 
rise above the body to the full height of capitals while a seventh, t, falls a little short of this height. Five of 
the letters, g j p q y, have parts extending below the body as far as the stems of the other letters extend above. 
The remaining letters aceimnorsuvwxz have only the body, if we except the i which has a dot. The 
normal width of the small letters is about | of that of capitals. The f i j 1 r t are narrower while the m and w 
are greater than normal width. The ratio of normal width to height for capitals and the bodies of small letters 
should be about ^. 

235. While the uniform heights and widths of letters as shown in the plates are satisfactory for the 
ordinary small sizes, they will often need modification in the larger ones in order to secure uniformity in apparent 
size. For instance, if the letters A B R S are all of the same width, the A will appear narrower than the B 
and the S than the R. When such is the case, the letter which seems narrow should be widened enough to over- 
come its defect. In the same way the C G and Q may appear a little too short especially when placed to the 
left of a letter like the B or E. 

236. If lower case letters are being used, the common rules relating to use of capitals should be followed. 
Words requiring Emphasis may be Capitalized, either on the Initial or THROUGHOUT. If capitals only are 
used THEY MAY BE ALL OF THE SAME HEIGHT or Initials may be Larger on the Prominent 
Words. A word of minor importance like the "of" Fig. 43, Title 1, line 2, would not have an enlarged initial 
unless it stood first in the line like "The" in the fourth line of the same title. When large and small capitals 
are thus used, the small ones should be about f the height of the large ones. As they have no parts 
extending below the base line, capitals permit the use of a larger letter for a given vertical space than 
is possible where lower case letters are used. This is frequently of importance when condensing material in 
a table. 

80 



Worcester 
Polytechnic 



237. When letters and spaces are narrowed to less than normal width as compared with their height, they 
are said to be COMPRESSED; when thej^ are made greater than normal width, they are said to be EXTENDED. 
Extended lettering will often look better than the normal as errors in parallelism are not so noticeable. The 
printer specifies a letter height by points. These range from 5 J to 72 point in metal sizes and a limited range 
of these is shown in Fig. 42. 

238. Slant of Letters. Uniformity in the slant of letters is essential. Letters may be vertical as in 
''Worcester," may slant forward like common handwriting as in " Pohi^echnic " or backward as in "Institute." 

See Fig. 38. The vertical form is the most difRcult as even an untrained ej'e 
notes slight variations from the erect position. The forward slant is most used, 
especially for rapid work. The inclination is about 22° from the vertical or a 
rise of 5 on a base of 2. See Fig. 37, line 4. A beginner will sometimes do 
better with the back slant than with either of the others. It should always 
\ V v Q^-r- X -r- X \ "T r" be tried, especially if the writer is left-handed. 

\\^^ \ \ \ \j \ v_ It is customary to draw the top and bottom limiting lines for lettering 

^'^- ^^- of any kind. The slant of letters is determined by reference to these lines 

whether they be straight or cm'ved. For instance, the limit lines for "Map of" 

on Fig. 43, Title 2, are arcs of concentric circles. In map drawings it is often 

necessaiy to use irregular curved limit lines as in "Salisbmy St.," Fig. 39. 

Note that the parts of the letter which lie on the limit lines in straight lettering 

are found coinciding with the limit lines in curved lettering. In the same way 

the slant of any particular letter will be determined by the direction of the curve 

at its position. Sometimes however in ornamental work, vertical letters are 

used as in "Bowtox," Fig. 39. 

239. Styles of Letters. There should be iniiformity in the style of letters employed for the same body 
of text and usually for the entire drawing. Variation in styles is permissible in titles or for purposes of classi- 
fication. As to the latter, in case of maps for instance, state names might be in one style, cities and towns 

81 




Fig. 39. 



in another. The tendency however is toward uniformity even here, with variation in the size or slant only for 
different features. 

240. A common error is the mixture of capitals and small letters indiscriminately thus, Drop ForoinGs; 
or the mixture of Roman and Gothic, thus LATHE. 

241. Spacing of Letters and Words. We must have uniformity in the apparent spaces between letters 
and the actual spaces between words. For small letters not exceeding J" high, in which the upright part is 
formed with a single penstroke, the normal space width may be j or | of the normal lettei width. That a defi- 
nite rule generally applicable ca^nnot be formulated is shown by the word "SMELTER," Fig. 40 upper line, in 

_^ which the spaces between letters are all equal. On account of the large area 

C? K A ^ I U L—P between the L and T, the word appears to be broken in two parts. If this 

^<-^ I V 1 1 — I — I I — I I space is reduced enough to give the appearance of uniform spacing, as in the 
^-^K J I — I — T" I — I — ) second line, we find that the T actually overhangs the L. The same modifica- 
/^ \/ [ r li tion of spacing will be necessary with the various combinations of A C F J L 

P Q T V AV and Y which, it will be noted, are the letters that do not fill out 
their parallelograms. Space letters so they appear to be evenly distributed 
throughout the word. If we drop a letter out of a word thus, Labo atory, the space between the and A is the 
requisite amount for readable spacing of words. A good phrase to remember is, " Crowd letters ; spread words." 
It is natural to do the reverse. If, as sometimes happens, it is impossible to provide a proper amovmt of space, 
the division into words may be effected by using a large capital initial for each word. Extra space must be 
allowed for punctuation marks between letters or words. Title 3, Fig. 43, shows an exception to rules for spacing. 

DESCRIPTION OF ALPHABETS 

242. Two alphabet styles, the Roman, Fig. 41, lines 1 and 2, and the single stroke inclined Gothic, 
Fig- 37 lines 1, 4 and 7, are used more than any others for drawings pertaining to engineering. The Roman 
is used especially in topographical work and the single stroke Gothic for shop drawings. This sentence is printed 
In Gothic. The word "Simple," Fig. 41 line 11, is in Outline Gothic. In the same way we have Outline Roman 
and Inclined Roman or Italic. The alphabet given in Fig. 41, lines 3 and 4, is a modification of the latter suitable 

82 



/ ABCDEFGHIJKLMNOPORSTUVWXYZ& 

2 abcdefghijklmnopqrstuvwxjz 123456789 

J ABGDEFGHIJKLMNOPQRSWVWXYZ& 

4 ah cdcfqhijklmnopcirstuvwxyz 125456789 

^ ABCDEFGniJKLriNOPQRSTVVWXTZ 
6 LOOKS-BESTCOAPRESSED -^ « 123456769 

7A^(S0E:rGhnXLn/10PQRST^VWXYZ 

(5 5vloedeFgQiikln?f2opG|r6havwxy^ 12(3. 4-56789 

// SIMPLE yjETHODS SUJTASLr FOR 

Fig. 41. 



for single stroke work. A single stroke Gothic capital may be changed to the Roman by the addition of serifs. 
the short horizontal terminals; kerns, the short terminals projecting from one side of the line and by increasing 
the line width on certain parts thus, A to A, E to E. The Roman is a more elaborate letter than the Gothic, 
requires more time to make and is therefore less suitable for rapid work. The single stroke inclined Gothic 
being the one most easily understood and acquired is the style best adapted for the beginner's first attempt. 
It illustrates all the cardinal principles of good lettering and it is but a step from this to the Roman, thence 
to other more elaborate forms. See an analysis of it in detail under the topic, "Directions for Practice Work." 

The letters shown in Fig. 37, lines 9 and 10, are adapted to either free-hand or mechanical construction, 
but especially the latter as there are no. curved parts. Lower case letters of the same style may be used, but 
they are not satisfactory from the standpoint of appearance and economy of time. Note that the heavy shad- 
ing is on the top and bottom horizontals only. 

In lines 1 and 2, Fig. 41, we have the vertical Roman. These letters must be formed with considerable 
care if they are to be presentable. Lack of parallelism, either in the general outlines or in the edges of shaded 
parts detracts much. The serifs too, must curve very nicely into the parts they terminate. If they are tilted, 
the result is markedly offensive. The letters in lines 3 and 4 Fig. 41 have already been referred to as modifi- 
cations of the Roman letter suited to off-hand work. 

While most styles of letters look well in the vertical, forward or back slant position, those shown in lines 5 to 
10, Fig. 41, are satisfactory only when vertical. They are free in style, easily made and as such well adapted 
to architectural drawings. Those shown in line 5 look best compressed. Of the three, that given in lines 7 and 
8 permits most rapid work. 

In lines 11 and 12, Fig. 41, are indicated some of the possibilities in the way of adorning so plain a letter 
as the Gothic. The simpler the treatment the more pleasing the result. Many other modifications will suggest 
themselves and for those who lack originality, a look through the magazine advertisers may afford inspiration. 

243. Old English. Fig. 42, is used chiefly for engrossing diplomas, certificates of membership and sim- 
ilar documents. Round Writing, not given here, has been used to some extent for working drawings, but though 
it can be rapidly made, looks well and is easily learned, its lack of legibility has prevented its general adoption. 

84 





Ci«jii|||tf| 









abtliffjiijiiliniioiqrst 
ttbh)o^l23i5678ffO 

30 POINT 

36 POINT 



6 POINT 
8 POINT 

10 POINT 

12 POINT 



14 POINT 

18 POINT 

24 POINT 



Fig. 42. 



85 



TITLES 

244. General Character. A general title contains the principal information necessary to identify 
the drawing with the matter represented. Its location will vary according to the character of the 
drawing, being most frequently in the lower right hand corner. The size of title space depends on the size of 
sheet, those given in Fig. 43 being appropriate for sheets up to 18" x 24" in size. For a sheet 24" x 36", the 
title and letter dimensions could be increased 50% or more. The shape of title space is determined by the kind 
of drawing and the contents of the title, but it is usually rectangular with the long dimension horizontal. Its 
arrangement will be symmetrical with respect to a vertical center line. Vertical letters produce the best effect 
in a title and a mixture of vertical and inclined letters is not satisfactory. The size of letters and spaces between 
lines should be so selected that the title will appear well balanced or distributed over the space. The several 
parts of the title may be lettered to correspond to their importance, proper prominence being obtained by judi- 
cious use of different sizes and styles. See Fig. 43, titles 1 and 2. Let the style of letters be appropriate to the 
character of the drawing; the fewer the styles in one title the better. 

245, Titles for Working Drawings. The title for a working drawing will specify the name of the machine 
or structure represented and generally the group of parts to which the sheet is devoted. If the machine or struc- 
ture is for some special use or location, it is often so stated. To this is added the name and location of the 
makers, the scale and date of the drawing with the name or initials of the draftsman who made it. In many 
titles, spaces are left for the signature, by initials only, of those who trace, check and approve the drawing. 
Occasionally we find the name of the designer attached. The job or order number is also often placed in the 
title. Title 1 of Fig. 43 is a form suitable for working drawings. Titles for this class of drawings are almost invari- 
ably placed in the lower right hand corner close up to the border. They can then be referred to conveniently 
when filed in a drawer with many others. Every drafting office has its own standard title form and this is 
of such shape and size as will meet its special needs. Though fanciful lettering is sometimes found on commercial 
drawings, the general tendency is toward extreme simplicity. The plain Gothic, either heavy face or single 
stroke, is the prevalent style employed and the largest letters will rarely exceed ^" in height. 

86 



246. Map Titles. The title of a map or plan specifies the locality represented, the scale and date of 
the drawing, name of the draftsman and usually the name of the surveyor or engineer. If the drawing has been 
made for a public commission or corporation, it is customaiy to include the name. The location, size and shape 
of the title will be determined by the available space outside of or even on the map. A unifonn arrangement 
for a series is not generally possible unless a one or two line title is used. Roman and Gothic letters, plain or 
simply modified, are the ones commonly used, but it is quite permissible to arrange them to produce an orna- 
mental effect. Title 2, Fig. 43, will illustrate this. It also shows how to grade the prominence of different 
parts of the title. For instance, "The World" if in solid black would give too heavy, while if in outline onl}' 
it would give too light an effect. As the most important part of the title it has larger letters. 

247. Architectural Titles. Titles for architectural drawings follow no rule, but are treated with great 
freedom. In the majority of cases, such a title will designate "what" and "where" regarding the matter repre- 
sented, also the scale of the drawing. It may or may not have the date, name of the architect, draftsman or 
other interesting infonnation. Its location is as variable as its contents and it is liable to be placed anywhere, 
even on the face of the drawing if such an arrangement is feasible. The size is usually such as to make it incon- 
spicuous. In fact, it is often made to resemble a formal title as little as possible. As to shape, the rectan- 
gular is most common and the long dimension will frequently be vertical, especially if the style be that shown in 
title 3, Fig. 43. In this form, the rectangle is to be filled as completely as possible without reference to punctu- 
ation or the division and spacing of words. Outline Roman, Old Roman and the styles shown in lines 5 to 8, 
Fig. 44, are the ones most used. 

248. Laying out Titles. To locate symmetrically a line of letters in a title gives beginners some trouble. 
If the letters are pencilled first, they can be located by trial, but this is apt to be a tedious process if the 
line be a long one or the letters other than the simplest. Consider for example in title 2, Fig. 43, the line, 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ' 

ON MERCATO r's PROJECTION. Numbering from the left and counting a space between words as 
equivalent to a letter there are seen to be 23 letters and spaces. If letter widths are all normal, number 12, the 
S in Mercator's would be at the middle of the line. Eut as there is a wide letter, number 4, and a wide space 
87 



2% 



<0 

5 






o> 



Pi 

«) 

o 

I 









09 5Q 



I 



S3 








Q ^^ 






Fig. 43. 



•o 



for the apostrophe at the left of the S, while at the right are two narrow letters, numbers 17 and 21, it is 
necessary to shift the center of the line a little to the left of the S. Starting then with the S properly placed, 
work both ways from the center. If appearances indicate that the end letters are not coming just right, a 
slight modification in letter and space widths will overcome the error as the work proceeds. It will be easier 
for some to first mark off in pencil the space allotted to each letter. On account of the difficulty of proper 
placing, it is advisable for beginners to pencil titles before inking, until the eye is sufficiently trained to dispense 
with it. 

DIRECTIONS FOR PRACTICE WORK 

249. Smooth hard surface paper is the best for lettering as it helps insure a clean cut line and smooth 
working of the pen. This is quite desirable when lettering for reproduction. When tracing cloth is used, the 
surface must be thoroughly rubbed with powdered chalk or pumice and all particles removed before the ink is 
applied. 

250. A fine pen like a Gillott Lithographic is best for Roman letters and others having fine lines and 
shaded parts. For single stroke Gothic, a medium fine pen that has been somewhat used or a fine ball point 
pen will work well. The prudent draftsman will take good care of his lettering pen, using it for no other pur- 
pose. It should be cleaned frequently as ink particles collect and dry between the nibs, spreading them so as 
to render the pen useless. Water-proof black ink is most used. 

251. The upper and lower guide lines are always pencilled and to save time in practice, cross-section 
paper ruled in tenths of an inch may be used. Slant lines in pencil showing the 
inclination may be ruled in intervals all over the sheet. A rise of 5 on a base 
of 2 is a very good inclination to use. Tack the sheet on the board in such a wa)^ 
that the elbow is supported when at work, otherwise the motion will be cramped, j^ /~ / /^ '^ /^ \ /~^ 

252. Practice first the strokes shown in Fig. 44, taking them in order, fj^ O C^ -/ / C / s / 

They will assist in acquiring the necessary swing. Blackboard practice on these Fig. 44. 

is very beneficial. It is needless to say, that at first, the mind must be concentrated on the pen point from 
89 





the start to the completion of a stroke. After considerable practice, it will be possible to letter automatically 
just as we write, but until that time it is well to remember that lettering is a mind as well as a hand exercise. 

253. Turning now to the alphabet of capitals in Fig. 37, lines 1 to 6, make two or three copies of each 
letter and figure. Before making a letter, note carefully in each case its general shape and proportions. The 
horizontal lines and enclosing parallelograms will assist in this. The parallelograms should always be sketched 
in pencil if the letter gives trouble as is generally the case with those having oblique parts like A, K, etc. 

254. Next study the sequence of strokes as shown in lines 2, 3, 5 and 6. Where two methods are given, 
the first is desirable for rapid work, but if the beginner does not master it at once, let him try the second. Other 
ways than those given may be used if they produce good results. After going through the capitals in this fashion, 
look over the work critically, mark the letters with which you have had the least success and devote extra prac- 
tice to them. It may be said here that the enjoyable way to learn to letter is not to practice half a day at a 
time once a month, but rather to spend a quarter-hour each day. Practice on the letters by groups is also desir- 
able. Thus the AKMNVWXYZ may be classed as the ones with predominating oblique parts, the B D E F 
H L P R T as the ones with horizontal parts, while C, G, and Q belongs to the ovals, leaving the I, J and S 
as miscellaneous. Attention has been directed to the I, J, M and W as letters of abnormal width. Other peculi- 
arities should be noticed as follows. The mid-horizontal parts of the A and G and the intersection point in the 
Y are the same height, a little below the middle. The corresponding parts in the B E F H R and X are slightly 
above the middle while in the P it is at the middle. The upper lobe in the B and the S is slightly smaller tl;ian 
the lower one. Invert- the letters to see it plainly. The lower oblique part- of the K if extended will intersect 
the top end of the upright part. The M and W must be carefully distinguished as it is a common error for a 
student to make an M like an inverted W, and vice versa. Among the figures, the upper part in the 3 and 8 
is smaller than the lower. The 9 is the 6 inverted and the general outline of each coincides with that of the zero. 

255. Lower case letters are to be practiced in the same way as the capitals. Those of abnormal width, 
the f i j 1 m r t and w, have already been mentioned. In the abcdegopq are ovals and straight parts, in 
the f h j m and n are hooks and straight parts while the u v w x and z are like their capitals. Note that the 

90 



cross-piece for the f and t is on a level with the tops of the short letters and that the upper oblique paii. of the 
k terminates at the same height. 

256. When an ink line is led out of another not dry and the angle is small, a blot may form at the notch 
as is indicated in Fig. 45. Such blotting as shown in the word "pen" may be 

avoided by carrying less ink on the pen or by breaking up the stroke as is /O/^ A7 '//^^)y/^^//^/jj 

shown in the second part of the same figure. The principle is to lead into, but j n A / 

not out of a wet line. This blotting is less liable in the Reinhardt letter than in 
the single stroke Gothic. ^'s. 45. 

257. If the beginner has no immediate success with letters of normal width, let him try the extended 
form, making his width equal to or greater than the height. 

258. The prominence of poor lettering may sometimes be reduced by heavy underlining. 

259. Practice lettering in pencil is not advisable when ink is at hand as it permits thoughtless work 
on account of being so easily corrected. 

260. It is useless to attempt free-hand lettering with chilled hands or immediately after severe muscular 
exertion. 

LETTERING FOR PHOTO REPRODUCTION 

261. A drawing may be reduced even to microscopic size by photography, but the chemical and mechan- 
ical manipulation necessary in producing the metal plate used for printing imposes some limits. For many draw- 
ings, it is desirable to have the final print smaller than the original because the unavoidable irregularities of 
free-hand work are thereby reduced in prominence. Some draftsmen, however, prefer little or no reduction 
because the effect of the original may be materially changed. The amount of reduction possible is really decided 
by the width of the finest lines, as beyond a certain point they will become broken in the plate. A reduction 
\6\ or \ the linear dimensions of the original is a good one, suitable for the width of medium weight pen strokes. 

91 



G^db c/gp q 



Fig. 43 is of the same size as the original, Figs. 37 and 41 are \ the hnear dimensions of the original while the 

cuts in the text are ^. a reduction to a size less than that of six point (ype used in this sentence will generally be unsatisfactory on the 

score of legibility. For the Same reason the spacing for very small letters should be more open. Notches and small 

loops have a tendency to fill when the letters are small and it was to avoid this that the Reinhardt letter was 

evolved and is used on its cuts by the "Engineering News." It is only a slight 
modification of the single stroke Gothic and all the letters which differ materially 
are shown in Fig. 46. The principal variation is in the slant of the ovals which 
^-j— ^ ' 'is about 45° as indicated, while in the Gothic letter the corresponding slant 

/ ' ^ ~^ C~^ Ol ^^^^^ b^ about 60°. Compare with line 7, Fig. 37. Another variation is in the 

// /// n (—. L/ C/ w/ hooks of letters such as the h, m and n where the hook is made more pointed 

and leads from the straight stem at a greater angle. Loops are also exaggerated 
as in the e. The upper and lower parts of the 2, 3, 6 and 9 are more nearly 

the same size. . . 

262. Waterproof black ink is the best to use for reduction work as there is no danger of blurring it by 
accidental moistening. All ink lines must be jet black, never grayish. Red coloring matter is sometimes put 
in the ink to insure its photographing properly. For the same photographic reason the paper used should be 
of a bluish rather than of a yellowish tinge. 

ALTERATIONS 

263. Often a letter or part of one must be removed. The use of an ink eraser is apt to demolish parts 
of neighboring letters, but it will leave a better surface for re-inking than will a sharp knife. It is best to pencil 
what is to be replaced and then use very little ink on the pen, otherwise the lines may have frayed edges. If 
a small part is to be removed, a sharp knife will be most satisfactory. First cut lightly the surface of the paper 
at the boundary of the erasure, being careful not to cut through. Then scrape carefully up to the edge of this 
cut and you will leave a sharp clean edge to the ink line. If the surface is such as would be spoiled by erasure, 
the parts can be painted over with " Chinese white" and ink applied on this. 

92 



264. BOOKS ON LETTERING 

Text Books for Students 

Lettering for Draftsmen. C. W. Reinhardt. Text 32 pages. 9 Plates. D. Van Nostrand Co. 
The Theory and Practice of Lettering. C. E. Sherman. Text 49 pages. 10 Plates. Midland Publishing Co. 
Free-Hand Lettering. V. T. Wilson. Text 95 pages. 23 Plates. John Wiley & Sons. 
Text-Book on Plain Lettering. H. S. Jacoby. Text 82 pages. 48 Plates. The Engineering News Pub- 
lishing Co. 
Free-Hand Lettering. F. T. Daniels. Text 34 pages. 13 Plates. D. C. Heath & Co. 

Collections of Alphabets suitable for engravers, jewelers, stone-cutters and sign writers. Chiefly mechanical 
in character. 

A Set of Alphabets. Copley. 47 Plates. 

Standard Alphabets. Prang. 34 Plates. 

Examples of Modern Alphabets. Delamotte. 48 Plates. 

Draughtsman's Alphabets. Esser. 21 Alphabets. 

Lettering as a Decorative Art 

Letters and Lettering. F. C. Brown. Text 214 pages. 211 illust. Bates & Guild Co. 
Alphabets. E. F. Strange. Text 294 pages. 197 illust. Geo. Bell & Sons. 

Contains also a good list of references. 
Alphabets Old and New. L. F. Day. Text 39 pages. 178 illust. Charles Scribner's Sons. 



93 



The Davis Press 
Worcester 



\0 """ 



WmWMM "-IBRARY OF CONGRESS 



019 936 894 1 




